GoDaddy - Microbusiness Density Forecasting
Mohammad Solki
2023-02-28
1. Introduction
1.1. Goal of the Competition
The challenge in this competition is to forecast microbusiness activity across the United States, as measured by the density of microbusinesses in US counties. Microbusinesses are often too small or too new to show up in traditional economic data sources, but microbusiness activity may be correlated with other economic indicators of general interest.
This work will help policymakers gain visibility into microbusinesses, a growing trend of very small entities. Additional information will enable new policies and programs to improve the success and impact of these smallest of businesses.
GoDaddy’s Venture Forward team has gathered data on over 20 million microbusinesses in the United States, defined as businesses with an online presence and ten or fewer employees, to help policymakers understand the factors associated with these small businesses. While traditional economic data sources often miss these businesses, GoDaddy’s survey data can provide insights into this sector of the economy. The data can be used to improve predictions and inform decision-making to create more inclusive and resilient economies. The competition hosted by GoDaddy aims to empower entrepreneurs by giving them the tools they need to grow online and make a substantial impact on communities across the country.
Model accuracy will be evaluated on SMAPE (Symmetric mean absolute percentage error) between forecasts and actual values. We define SMAPE = 0 when the actual and predicted values are both 0.
SMAPE formula is usually defined as follows:
\[ \text{SMAPE} = \frac{100\%}{n} \sum_{t=1}^{n} \frac{\left\lvert F_t - A_t \right\rvert}{( \left\lvert F_t \right\rvert + \left\lvert A_t \right\rvert)/2} \]
where:
\(n\) is the number of observations in the time series
\(F_t\) is the forecasted value at time \(t\)
\(A_t\) is the actual value at time \(t\)
\(\left\lvert x \right\rvert\) denotes the absolute value of \(x\).
1.2. Datasets
A great deal of data is publicly available about counties and we have not attempted to gather it all here. You are strongly encouraged to use external data sources for features.
train.csv
row_idAn ID code for the row.cfipsA unique identifier for each county using the Federal Information Processing System. The first two digits correspond to the state FIPS code, while the following 3 represent the county.county_nameThe written name of the county.state_nameThe name of the state.first_day_of_monthThe date of the first day of the month.microbusiness_densityMicrobusinesses per 100 people over the age of 18 in the given county. This is the target variable. The population figures used to calculate the density are on a two-year lag due to the pace of update provided by the U.S. Census Bureau, which provides the underlying population data annually. 2021 density figures are calculated using 2019 population figures, etc.activeThe raw count of microbusinesses in the county. Not provided for the test set.
test.csv Metadata for the submission rows. This file will remain unchanged throughout the competition.
row_idAn ID code for the row.cfipsA unique identifier for each county using the Federal Information Processing System. The first two digits correspond to the state FIPS code, while the following 3 represent the county.first_day_of_monthThe date of the first day of the month.
census_starter.csv Examples of useful columns from the Census Bureau’s American Community Survey (ACS) at data.census.gov. The percentage fields were derived from the raw counts provided by the ACS. All fields have a two year lag to match what information was avaiable at the time a given microbusiness data update was published.
pct_bb_[year]The percentage of households in the county with access to broadband of any type. Derived from ACS table B28002: PRESENCE AND TYPES OF INTERNET SUBSCRIPTIONS IN HOUSEHOLD.cfipsThe CFIPS code.pct_college_[year]The percent of the population in the county over age 25 with a 4-year college degree. Derived from ACS table S1501: EDUCATIONAL ATTAINMENT.pct_foreign_born_[year]The percent of the population in the county born outside of the United States. Derived from ACS table DP02: SELECTED SOCIAL CHARACTERISTICS IN THE UNITED STATES.pct_it_workers_[year]The percent of the workforce in the county employed in information related industries. Derived from ACS table S2405: INDUSTRY BY OCCUPATION FOR THE CIVILIAN EMPLOYED POPULATION 16 YEARS AND OVER.median_hh_inc_[year]The median household income in the county. Derived from ACS table S1901: INCOME IN THE PAST 12 MONTHS (IN 2021 INFLATION-ADJUSTED DOLLARS).
2. Setup the Environment
First, we’ll set the working directory using
setwd(), and then import the required
libraries. As we proceed through the report the list of libraries might
change.
# Set the working directory
setwd("/Users/dreamer/Downloads/Godaddy/godaddy_microbusiness_forecasting")# Importing the libraries
# Recognize package conflicts
library(conflicted)
# Multi-purpose package for data import, tidying, manipulation, visualisation, and programming
# Most common packages include: ggplot2, purrr, tibble, dplyr, tidyr, stringr, readr, forcats
library(tidyverse)
# Deal with missing data
library(mice)
# Related to plots
library(maps)
#library(ggmap)
library(gridExtra)
library(mapdata)
library(ggcorrplot)
library(corrplot)
# Training
library(caret)
library(gbm)
# Color palette
library(viridis)
# Future Selection
#library(KernSmooth)
library(glmnet)
library(randomForest)
# libraries required for calculating SMAPE
library(forecast)
library(Metrics)3. Exploratory Data Analysis
3.1. Exploring the datasets
Explore the datasets to get a better understanding of the data.
Load the train, test, and
census_starter datasets into R dataframes.
# Load train.csv into a dataframe
train_df <- read.csv("./datasets/train.csv")
# Load test.csv into a dataframe
test_df <- read.csv("./datasets/test.csv")
# Load census_starter.csv into a dataframe
census_df <- read.csv("./datasets/census_starter.csv")After reading the CSV files into dataframes, we should check whether
the data is loaded correctly or not. We can use the head()
function of R to display the first few rows of the dataframes and
tail() function to display the last rows. This will display
the first and last six rows of the train,
test and census dataframes. We can
also use other R functions such as str() and
summary() to get more information about the dataframes,
such as column names, data types, and summary statistics.
# Display the first 6 rows of the dataframes
head(train_df)## row_id cfips county state first_day_of_month
## 1 1001_2019-08-01 1001 Autauga County Alabama 2019-08-01
## 2 1001_2019-09-01 1001 Autauga County Alabama 2019-09-01
## 3 1001_2019-10-01 1001 Autauga County Alabama 2019-10-01
## 4 1001_2019-11-01 1001 Autauga County Alabama 2019-11-01
## 5 1001_2019-12-01 1001 Autauga County Alabama 2019-12-01
## 6 1001_2020-01-01 1001 Autauga County Alabama 2020-01-01
## microbusiness_density active
## 1 3.007682 1249
## 2 2.884870 1198
## 3 3.055843 1269
## 4 2.993233 1243
## 5 2.993233 1243
## 6 2.969090 1242head(test_df)## row_id cfips first_day_of_month
## 1 1001_2022-11-01 1001 2022-11-01
## 2 1003_2022-11-01 1003 2022-11-01
## 3 1005_2022-11-01 1005 2022-11-01
## 4 1007_2022-11-01 1007 2022-11-01
## 5 1009_2022-11-01 1009 2022-11-01
## 6 1011_2022-11-01 1011 2022-11-01head(census_df)## pct_bb_2017 pct_bb_2018 pct_bb_2019 pct_bb_2020 pct_bb_2021 cfips
## 1 76.6 78.9 80.6 82.7 85.5 1001
## 2 74.5 78.1 81.8 85.1 87.9 1003
## 3 57.2 60.4 60.5 64.6 64.6 1005
## 4 62.0 66.1 69.2 76.1 74.6 1007
## 5 65.8 68.5 73.0 79.6 81.0 1009
## 6 49.4 58.9 60.1 60.6 59.4 1011
## pct_college_2017 pct_college_2018 pct_college_2019 pct_college_2020
## 1 14.5 15.9 16.1 16.7
## 2 20.4 20.7 21.0 20.2
## 3 7.6 7.8 7.6 7.3
## 4 8.1 7.6 6.5 7.4
## 5 8.7 8.1 8.6 8.9
## 6 6.6 7.4 7.4 6.1
## pct_college_2021 pct_foreign_born_2017 pct_foreign_born_2018
## 1 16.4 2.1 2.0
## 2 20.6 3.2 3.4
## 3 6.7 2.7 2.5
## 4 7.9 1.0 1.4
## 5 9.3 4.5 4.4
## 6 8.1 1.8 0.9
## pct_foreign_born_2019 pct_foreign_born_2020 pct_foreign_born_2021
## 1 2.3 2.3 2.1
## 2 3.7 3.4 3.5
## 3 2.7 2.6 2.6
## 4 1.5 1.6 1.1
## 5 4.5 4.4 4.5
## 6 0.7 1.5 1.2
## pct_it_workers_2017 pct_it_workers_2018 pct_it_workers_2019
## 1 1.3 1.1 0.7
## 2 1.4 1.3 1.4
## 3 0.5 0.3 0.8
## 4 1.2 1.4 1.6
## 5 1.3 1.4 0.9
## 6 0.4 0.3 0.5
## pct_it_workers_2020 pct_it_workers_2021 median_hh_inc_2017 median_hh_inc_2018
## 1 0.6 1.1 55317 58786
## 2 1.0 1.3 52562 55962
## 3 1.1 0.8 33368 34186
## 4 1.7 2.1 43404 45340
## 5 1.1 0.9 47412 48695
## 6 0.3 0.2 29655 32152
## median_hh_inc_2019 median_hh_inc_2020 median_hh_inc_2021
## 1 58731 57982 62660
## 2 58320 61756 64346
## 3 32525 34990 36422
## 4 47542 51721 54277
## 5 49358 48922 52830
## 6 37785 33866 29063# Display the last 6 rows of the dataframes
tail(train_df)## row_id cfips county state first_day_of_month
## 122260 56045_2022-05-01 56045 Weston County Wyoming 2022-05-01
## 122261 56045_2022-06-01 56045 Weston County Wyoming 2022-06-01
## 122262 56045_2022-07-01 56045 Weston County Wyoming 2022-07-01
## 122263 56045_2022-08-01 56045 Weston County Wyoming 2022-08-01
## 122264 56045_2022-09-01 56045 Weston County Wyoming 2022-09-01
## 122265 56045_2022-10-01 56045 Weston County Wyoming 2022-10-01
## microbusiness_density active
## 122260 1.803249 101
## 122261 1.803249 101
## 122262 1.803249 101
## 122263 1.785395 100
## 122264 1.785395 100
## 122265 1.785395 100tail(test_df)## row_id cfips first_day_of_month
## 25075 56035_2023-06-01 56035 2023-06-01
## 25076 56037_2023-06-01 56037 2023-06-01
## 25077 56039_2023-06-01 56039 2023-06-01
## 25078 56041_2023-06-01 56041 2023-06-01
## 25079 56043_2023-06-01 56043 2023-06-01
## 25080 56045_2023-06-01 56045 2023-06-01tail(census_df)## pct_bb_2017 pct_bb_2018 pct_bb_2019 pct_bb_2020 pct_bb_2021 cfips
## 3137 82.9 81.7 85.6 88.1 89.8 56035
## 3138 82.2 82.4 84.0 86.7 88.4 56037
## 3139 83.5 85.9 87.1 89.1 90.5 56039
## 3140 83.8 88.2 89.5 91.4 90.6 56041
## 3141 76.4 78.3 78.2 82.8 85.4 56043
## 3142 71.1 73.3 76.8 79.7 81.3 56045
## pct_college_2017 pct_college_2018 pct_college_2019 pct_college_2020
## 3137 19.2 19.0 16.7 21.7
## 3138 15.3 15.2 14.8 13.7
## 3139 37.7 37.8 38.9 37.2
## 3140 11.9 10.5 11.1 12.6
## 3141 15.4 15.0 15.4 15.0
## 3142 14.1 13.5 13.4 12.7
## pct_college_2021 pct_foreign_born_2017 pct_foreign_born_2018
## 3137 20.9 3.9 3.1
## 3138 12.4 5.0 5.3
## 3139 38.3 10.8 11.2
## 3140 12.3 2.9 3.1
## 3141 17.2 2.3 1.4
## 3142 13.9 3.8 4.1
## pct_foreign_born_2019 pct_foreign_born_2020 pct_foreign_born_2021
## 3137 4.4 5.1 5.1
## 3138 4.7 5.2 5.5
## 3139 11.8 11.4 11.1
## 3140 2.9 2.9 2.9
## 3141 1.6 2.2 1.0
## 3142 1.7 2.3 1.6
## pct_it_workers_2017 pct_it_workers_2018 pct_it_workers_2019
## 3137 0.1 0.0 0.0
## 3138 0.6 0.6 1.0
## 3139 0.7 1.2 1.4
## 3140 1.2 1.2 1.4
## 3141 1.3 1.0 0.9
## 3142 0.6 0.6 0.0
## pct_it_workers_2020 pct_it_workers_2021 median_hh_inc_2017
## 3137 0.0 0.0 84911
## 3138 0.9 1.0 71083
## 3139 1.5 2.0 80049
## 3140 1.7 0.9 54672
## 3141 0.9 1.1 51362
## 3142 0.0 0.0 59605
## median_hh_inc_2018 median_hh_inc_2019 median_hh_inc_2020
## 3137 78680 77403 78655
## 3138 73008 74843 73384
## 3139 83831 84678 87053
## 3140 58235 63403 72458
## 3141 53426 54158 57306
## 3142 52867 57031 53333
## median_hh_inc_2021
## 3137 82342
## 3138 76668
## 3139 94498
## 3140 75106
## 3141 62271
## 3142 65566# Display information about the train dataframe
str(train_df)## 'data.frame': 122265 obs. of 7 variables:
## $ row_id : chr "1001_2019-08-01" "1001_2019-09-01" "1001_2019-10-01" "1001_2019-11-01" ...
## $ cfips : int 1001 1001 1001 1001 1001 1001 1001 1001 1001 1001 ...
## $ county : chr "Autauga County" "Autauga County" "Autauga County" "Autauga County" ...
## $ state : chr "Alabama" "Alabama" "Alabama" "Alabama" ...
## $ first_day_of_month : chr "2019-08-01" "2019-09-01" "2019-10-01" "2019-11-01" ...
## $ microbusiness_density: num 3.01 2.88 3.06 2.99 2.99 ...
## $ active : int 1249 1198 1269 1243 1243 1242 1217 1227 1255 1257 ...#cat(rep("=", 40), "\n") # Print a line of 40 equal signs
summary(train_df)## row_id cfips county state
## Length:122265 Min. : 1001 Length:122265 Length:122265
## Class :character 1st Qu.:18177 Class :character Class :character
## Mode :character Median :29173 Mode :character Mode :character
## Mean :30376
## 3rd Qu.:45077
## Max. :56045
## first_day_of_month microbusiness_density active
## Length:122265 Min. : 0.000 Min. : 0
## Class :character 1st Qu.: 1.639 1st Qu.: 145
## Mode :character Median : 2.587 Median : 488
## Mean : 3.818 Mean : 6443
## 3rd Qu.: 4.519 3rd Qu.: 2124
## Max. :284.340 Max. :1167744# Display information about the test dataframe
str(test_df)## 'data.frame': 25080 obs. of 3 variables:
## $ row_id : chr "1001_2022-11-01" "1003_2022-11-01" "1005_2022-11-01" "1007_2022-11-01" ...
## $ cfips : int 1001 1003 1005 1007 1009 1011 1013 1015 1017 1019 ...
## $ first_day_of_month: chr "2022-11-01" "2022-11-01" "2022-11-01" "2022-11-01" ...#cat(rep("=", 40), "\n") # Print a line of 40 equal signs
summary(test_df)## row_id cfips first_day_of_month
## Length:25080 Min. : 1001 Length:25080
## Class :character 1st Qu.:18177 Class :character
## Mode :character Median :29173 Mode :character
## Mean :30376
## 3rd Qu.:45077
## Max. :56045# Display information about the census dataframe
str(census_df)## 'data.frame': 3142 obs. of 26 variables:
## $ pct_bb_2017 : num 76.6 74.5 57.2 62 65.8 49.4 58.2 71 62.8 67.5 ...
## $ pct_bb_2018 : num 78.9 78.1 60.4 66.1 68.5 58.9 62.1 73 66.5 68.6 ...
## $ pct_bb_2019 : num 80.6 81.8 60.5 69.2 73 60.1 64.6 75.1 69.4 70.7 ...
## $ pct_bb_2020 : num 82.7 85.1 64.6 76.1 79.6 60.6 73.6 79.8 74.5 75 ...
## $ pct_bb_2021 : num 85.5 87.9 64.6 74.6 81 59.4 76.3 81.6 77.1 76.7 ...
## $ cfips : int 1001 1003 1005 1007 1009 1011 1013 1015 1017 1019 ...
## $ pct_college_2017 : num 14.5 20.4 7.6 8.1 8.7 6.6 9.6 10.2 9 6.6 ...
## $ pct_college_2018 : num 15.9 20.7 7.8 7.6 8.1 7.4 9.7 10.2 9.3 6.8 ...
## $ pct_college_2019 : num 16.1 21 7.6 6.5 8.6 7.4 9.7 10.5 9.5 6.6 ...
## $ pct_college_2020 : num 16.7 20.2 7.3 7.4 8.9 6.1 10.1 10.5 10.5 6.3 ...
## $ pct_college_2021 : num 16.4 20.6 6.7 7.9 9.3 8.1 8.1 11.4 9.6 6.2 ...
## $ pct_foreign_born_2017: num 2.1 3.2 2.7 1 4.5 1.8 1 2.6 1.3 0.7 ...
## $ pct_foreign_born_2018: num 2 3.4 2.5 1.4 4.4 0.9 1.4 2.7 1.4 0.8 ...
## $ pct_foreign_born_2019: num 2.3 3.7 2.7 1.5 4.5 0.7 0.8 2.7 1.8 0.9 ...
## $ pct_foreign_born_2020: num 2.3 3.4 2.6 1.6 4.4 1.5 1.9 2.5 1.9 1.9 ...
## $ pct_foreign_born_2021: num 2.1 3.5 2.6 1.1 4.5 1.2 1.7 2.5 2 2 ...
## $ pct_it_workers_2017 : num 1.3 1.4 0.5 1.2 1.3 0.4 1.1 1.4 2.4 1.4 ...
## $ pct_it_workers_2018 : num 1.1 1.3 0.3 1.4 1.4 0.3 1.4 1.4 2.1 1.3 ...
## $ pct_it_workers_2019 : num 0.7 1.4 0.8 1.6 0.9 0.5 1.7 1.2 2.1 1.2 ...
## $ pct_it_workers_2020 : num 0.6 1 1.1 1.7 1.1 0.3 1.3 1 2.3 0.9 ...
## $ pct_it_workers_2021 : num 1.1 1.3 0.8 2.1 0.9 0.2 1.4 1 1.8 0.4 ...
## $ median_hh_inc_2017 : int 55317 52562 33368 43404 47412 29655 36326 43686 37342 40041 ...
## $ median_hh_inc_2018 : num 58786 55962 34186 45340 48695 ...
## $ median_hh_inc_2019 : int 58731 58320 32525 47542 49358 37785 40688 47255 42289 41919 ...
## $ median_hh_inc_2020 : num 57982 61756 34990 51721 48922 ...
## $ median_hh_inc_2021 : num 62660 64346 36422 54277 52830 ...#cat(rep("=", 40), "\n") # Print a line of 40 equal signs
summary(census_df)## pct_bb_2017 pct_bb_2018 pct_bb_2019 pct_bb_2020
## Min. :24.50 Min. :25.70 Min. :34.80 Min. :33.30
## 1st Qu.:64.20 1st Qu.:67.42 1st Qu.:70.50 1st Qu.:74.10
## Median :70.70 Median :73.60 Median :76.45 Median :79.60
## Mean :69.92 Mean :72.69 Mean :75.40 Mean :78.54
## 3rd Qu.:76.40 3rd Qu.:78.80 3rd Qu.:81.40 3rd Qu.:84.10
## Max. :94.60 Max. :95.50 Max. :96.00 Max. :97.10
## NA's :1
## pct_bb_2021 cfips pct_college_2017 pct_college_2018
## Min. :37.00 Min. : 1001 Min. : 2.40 Min. : 0.00
## 1st Qu.:76.40 1st Qu.:18178 1st Qu.: 9.70 1st Qu.: 9.90
## Median :81.70 Median :29176 Median :12.80 Median :13.00
## Mean :80.54 Mean :30384 Mean :13.81 Mean :14.01
## 3rd Qu.:85.90 3rd Qu.:45080 3rd Qu.:16.80 3rd Qu.:17.10
## Max. :97.60 Max. :56045 Max. :43.70 Max. :48.00
## NA's :1
## pct_college_2019 pct_college_2020 pct_college_2021 pct_foreign_born_2017
## Min. : 0.00 Min. : 0.00 Min. : 0.00 Min. : 0.000
## 1st Qu.:10.10 1st Qu.:10.50 1st Qu.:10.60 1st Qu.: 1.400
## Median :13.25 Median :13.60 Median :13.80 Median : 2.700
## Mean :14.24 Mean :14.63 Mean :14.85 Mean : 4.702
## 3rd Qu.:17.30 3rd Qu.:17.90 3rd Qu.:18.00 3rd Qu.: 5.700
## Max. :45.40 Max. :43.00 Max. :43.70 Max. :52.900
## NA's :1 NA's :1
## pct_foreign_born_2018 pct_foreign_born_2019 pct_foreign_born_2020
## Min. : 0.000 Min. : 0.000 Min. : 0.000
## 1st Qu.: 1.400 1st Qu.: 1.400 1st Qu.: 1.400
## Median : 2.700 Median : 2.700 Median : 2.800
## Mean : 4.725 Mean : 4.769 Mean : 4.749
## 3rd Qu.: 5.700 3rd Qu.: 5.700 3rd Qu.: 5.700
## Max. :53.300 Max. :53.700 Max. :54.000
## NA's :1
## pct_foreign_born_2021 pct_it_workers_2017 pct_it_workers_2018
## Min. : 0.000 Min. : 0.000 Min. : 0.000
## 1st Qu.: 1.400 1st Qu.: 0.800 1st Qu.: 0.800
## Median : 2.700 Median : 1.300 Median : 1.300
## Mean : 4.744 Mean : 1.427 Mean : 1.382
## 3rd Qu.: 5.700 3rd Qu.: 1.900 3rd Qu.: 1.800
## Max. :54.000 Max. :17.400 Max. :11.700
## NA's :1 NA's :1
## pct_it_workers_2019 pct_it_workers_2020 pct_it_workers_2021 median_hh_inc_2017
## Min. : 0.000 Min. : 0.000 Min. : 0.000 Min. : 19264
## 1st Qu.: 0.700 1st Qu.: 0.700 1st Qu.: 0.600 1st Qu.: 41123
## Median : 1.200 Median : 1.200 Median : 1.100 Median : 48066
## Mean : 1.339 Mean : 1.309 Mean : 1.273 Mean : 49754
## 3rd Qu.: 1.800 3rd Qu.: 1.800 3rd Qu.: 1.700 3rd Qu.: 55764
## Max. :10.500 Max. :15.200 Max. :15.200 Max. :129588
## NA's :1 NA's :1
## median_hh_inc_2018 median_hh_inc_2019 median_hh_inc_2020 median_hh_inc_2021
## Min. : 20188 Min. : 21504 Min. : 22292 Min. : 17109
## 1st Qu.: 42480 1st Qu.: 44155 1st Qu.: 45653 1st Qu.: 48180
## Median : 49888 Median : 51758 Median : 52842 Median : 55907
## Mean : 51583 Mean : 53476 Mean : 55012 Mean : 58223
## 3rd Qu.: 57611 3rd Qu.: 59867 3rd Qu.: 61501 3rd Qu.: 64930
## Max. :136268 Max. :142299 Max. :147111 Max. :156821
## NA's :1 NA's :2 NA's :2The data type of first_day_of_month column in
train_df and test_df is
character. We will convert the character to Date
format.
# Change first_day_of_month data type to Date
train_df$first_day_of_month <- as.Date(train_df$first_day_of_month)
test_df$first_day_of_month <- as.Date(test_df$first_day_of_month)
str(train_df$first_day_of_month)## Date[1:122265], format: "2019-08-01" "2019-09-01" "2019-10-01" "2019-11-01" "2019-12-01" ...3.2. Checking the Dataframes for Missing Values
The is.na() function is used to create a logical matrix
where TRUE represents a missing value and FALSE
represents a non-missing value. The colSums() function is
then used to count the number of missing values in each column of the
data frame. If the sum of a column is greater than 0, it means that
there is at least one missing value in that column.
# Check for missing values in the train data frame
colSums(is.na(train_df))## row_id cfips county
## 0 0 0
## state first_day_of_month microbusiness_density
## 0 0 0
## active
## 0# Check for missing values in the test data frame
colSums(is.na(test_df))## row_id cfips first_day_of_month
## 0 0 0# Check for missing values in the census data frame
colSums(is.na(census_df))## pct_bb_2017 pct_bb_2018 pct_bb_2019
## 0 0 0
## pct_bb_2020 pct_bb_2021 cfips
## 1 1 0
## pct_college_2017 pct_college_2018 pct_college_2019
## 0 0 0
## pct_college_2020 pct_college_2021 pct_foreign_born_2017
## 1 1 0
## pct_foreign_born_2018 pct_foreign_born_2019 pct_foreign_born_2020
## 0 0 1
## pct_foreign_born_2021 pct_it_workers_2017 pct_it_workers_2018
## 1 0 1
## pct_it_workers_2019 pct_it_workers_2020 pct_it_workers_2021
## 0 1 1
## median_hh_inc_2017 median_hh_inc_2018 median_hh_inc_2019
## 0 1 0
## median_hh_inc_2020 median_hh_inc_2021
## 2 2#{r fig.width=7, fig.align='center', fig.height=4, out.width='100%'}
# Calculate the number and percentage of missing values for each column
missing_data <- census_df %>%
summarise_all(~ sum(is.na(.))) %>%
gather(variable, missing_count) %>%
mutate(missing_percent = missing_count/nrow(census_df)*100)
# Create two plots side by side
plot1 <- ggplot(missing_data, aes(x = missing_count, y = variable)) +
geom_bar(stat = "identity", fill = "steelblue") +
labs(x = "Number of missing values", y = "") +
ggtitle("Number of missing values in census_df") +
theme_gray()
plot2 <- ggplot(missing_data, aes(x = missing_percent, y = variable)) +
geom_bar(stat = "identity", fill = "lightblue") +
labs(x = "Percentage of missing values", y = "") +
ggtitle("Percentage of missing values in census_df") +
theme_gray()
# Arrange the two plots side by side
grid.arrange(plot1, plot2, ncol = 2)
We use the complete.cases() function to determine which
rows have complete data and which rows have missing values. This
function returns a logical vector indicating which rows have no missing
values. Therefore, to identify the rows with missing values, we use the
! operator to negate the logical vector returned by
complete.cases(). Then, we use the is.na()
function to identify which columns have missing values for each missing
row:
# Identify rows with missing values in census_df
missing_rows <- which(!complete.cases(census_df))
# Identify columns with missing values for each missing row
for (i in missing_rows) {
cat("Row", i, "has missing values in columns:",
paste(names(census_df)[is.na(census_df[i,])], collapse = ", "), "\n")
}## Row 93 has missing values in columns: pct_bb_2020, pct_bb_2021, pct_college_2020, pct_college_2021, pct_foreign_born_2020, pct_foreign_born_2021, pct_it_workers_2020, pct_it_workers_2021, median_hh_inc_2020, median_hh_inc_2021
## Row 1817 has missing values in columns: pct_it_workers_2018, median_hh_inc_2018
## Row 2645 has missing values in columns: median_hh_inc_2020
## Row 2674 has missing values in columns: median_hh_inc_2021print(census_df[missing_rows,])## pct_bb_2017 pct_bb_2018 pct_bb_2019 pct_bb_2020 pct_bb_2021 cfips
## 93 80.5 79.1 80.4 NA NA 2261
## 1817 49.1 52.1 57.6 60.7 63.5 35039
## 2645 66.3 66.6 61.2 63.2 70.1 48243
## 2674 64.5 72.7 73.3 96.8 97.0 48301
## pct_college_2017 pct_college_2018 pct_college_2019 pct_college_2020
## 93 23.1 19.0 16.5 NA
## 1817 12.0 12.5 12.6 10.6
## 2645 18.4 16.0 10.8 14.3
## 2674 4.7 0.0 0.0 0.0
## pct_college_2021 pct_foreign_born_2017 pct_foreign_born_2018
## 93 NA 4.9 6.3
## 1817 10.1 4.5 3.7
## 2645 10.9 22.4 14.9
## 2674 0.0 10.8 15.7
## pct_foreign_born_2019 pct_foreign_born_2020 pct_foreign_born_2021
## 93 6.6 NA NA
## 1817 4.2 4.5 4.8
## 2645 20.9 10.1 12.7
## 2674 12.2 0.0 1.2
## pct_it_workers_2017 pct_it_workers_2018 pct_it_workers_2019
## 93 3.3 3.9 5.3
## 1817 0.8 NA 0.8
## 2645 0.0 0.0 0.0
## 2674 0.0 0.0 0.0
## pct_it_workers_2020 pct_it_workers_2021 median_hh_inc_2017
## 93 NA NA 86019
## 1817 0.4 0.7 33422
## 2645 0.0 0.0 46534
## 2674 0.0 0.0 80938
## median_hh_inc_2018 median_hh_inc_2019 median_hh_inc_2020
## 93 82306 79867 NA
## 1817 NA 39952 42264
## 2645 53194 53088 NA
## 2674 81875 83750 44076
## median_hh_inc_2021
## 93 NA
## 1817 46994
## 2645 38659
## 2674 NA3.3. Dealing with Missing Values
The mice package implements a method to
deal with missing data. The package creates multiple imputations
(replacement values) for multivariate missing data.
We’ll use the mice package to impute missing values in
the census_df dataframe with below arguments:
m: The number of imputations to generate was set to 5, because, generally, m should be set to at least 5 for good imputation performance. Creating too many datasets will increase the computational load and may not necessarily lead to better results.
maxit: The maxit value was set to 50 to allow for a larger number of iterations to ensure that the imputation algorithm converges and fills in missing values as accurately as possible.
method: In this case, we are using “pmm” which stands for Predictive Mean Matching, because it is a flexible and widely used imputation method that works well with continuous variables. The method estimates the missing values by drawing from a set of observed values that have similar characteristics to the missing values.
print: The print value is set to FALSE because this function prints a huge log output to console.
# Impute missing data using mice
imputed_data <- mice(census_df, m = 5, maxit = 50, method = "pmm", print = FALSE)
# Extract imputed data
imputed_data <- complete(imputed_data)# Check for missing values in imputed data
colSums(is.na(imputed_data))## pct_bb_2017 pct_bb_2018 pct_bb_2019
## 0 0 0
## pct_bb_2020 pct_bb_2021 cfips
## 0 0 0
## pct_college_2017 pct_college_2018 pct_college_2019
## 0 0 0
## pct_college_2020 pct_college_2021 pct_foreign_born_2017
## 0 0 0
## pct_foreign_born_2018 pct_foreign_born_2019 pct_foreign_born_2020
## 0 0 0
## pct_foreign_born_2021 pct_it_workers_2017 pct_it_workers_2018
## 0 0 0
## pct_it_workers_2019 pct_it_workers_2020 pct_it_workers_2021
## 0 0 0
## median_hh_inc_2017 median_hh_inc_2018 median_hh_inc_2019
## 0 0 0
## median_hh_inc_2020 median_hh_inc_2021
## 0 0# Check the filled missing values
print(imputed_data[missing_rows,])## pct_bb_2017 pct_bb_2018 pct_bb_2019 pct_bb_2020 pct_bb_2021 cfips
## 93 80.5 79.1 80.4 81.0 83.5 2261
## 1817 49.1 52.1 57.6 60.7 63.5 35039
## 2645 66.3 66.6 61.2 63.2 70.1 48243
## 2674 64.5 72.7 73.3 96.8 97.0 48301
## pct_college_2017 pct_college_2018 pct_college_2019 pct_college_2020
## 93 23.1 19.0 16.5 15.1
## 1817 12.0 12.5 12.6 10.6
## 2645 18.4 16.0 10.8 14.3
## 2674 4.7 0.0 0.0 0.0
## pct_college_2021 pct_foreign_born_2017 pct_foreign_born_2018
## 93 15.1 4.9 6.3
## 1817 10.1 4.5 3.7
## 2645 10.9 22.4 14.9
## 2674 0.0 10.8 15.7
## pct_foreign_born_2019 pct_foreign_born_2020 pct_foreign_born_2021
## 93 6.6 6.0 7.6
## 1817 4.2 4.5 4.8
## 2645 20.9 10.1 12.7
## 2674 12.2 0.0 1.2
## pct_it_workers_2017 pct_it_workers_2018 pct_it_workers_2019
## 93 3.3 3.9 5.3
## 1817 0.8 0.5 0.8
## 2645 0.0 0.0 0.0
## 2674 0.0 0.0 0.0
## pct_it_workers_2020 pct_it_workers_2021 median_hh_inc_2017
## 93 5.6 1.0 86019
## 1817 0.4 0.7 33422
## 2645 0.0 0.0 46534
## 2674 0.0 0.0 80938
## median_hh_inc_2018 median_hh_inc_2019 median_hh_inc_2020
## 93 82306 79867 78889
## 1817 36148 39952 42264
## 2645 53194 53088 42285
## 2674 81875 83750 44076
## median_hh_inc_2021
## 93 81817
## 1817 46994
## 2645 38659
## 2674 528423.4. Checking the Time Frame of train and test Dataframes
After dealing with the missing values, we have to check the time frame provided in the train and test datasets.
index <- unique(train_df$first_day_of_month)
print(index)## [1] "2019-08-01" "2019-09-01" "2019-10-01" "2019-11-01" "2019-12-01"
## [6] "2020-01-01" "2020-02-01" "2020-03-01" "2020-04-01" "2020-05-01"
## [11] "2020-06-01" "2020-07-01" "2020-08-01" "2020-09-01" "2020-10-01"
## [16] "2020-11-01" "2020-12-01" "2021-01-01" "2021-02-01" "2021-03-01"
## [21] "2021-04-01" "2021-05-01" "2021-06-01" "2021-07-01" "2021-08-01"
## [26] "2021-09-01" "2021-10-01" "2021-11-01" "2021-12-01" "2022-01-01"
## [31] "2022-02-01" "2022-03-01" "2022-04-01" "2022-05-01" "2022-06-01"
## [36] "2022-07-01" "2022-08-01" "2022-09-01" "2022-10-01"The training data time frame includes 08/2019 to 10/2022
index <- unique(test_df$first_day_of_month)
print(index)## [1] "2022-11-01" "2022-12-01" "2023-01-01" "2023-02-01" "2023-03-01"
## [6] "2023-04-01" "2023-05-01" "2023-06-01"The prediction dates provided include 11/2022 to 06/2023
3.5. Adding New Columns to train and test
To make analysis easier and be able to group the data by year and
month, we will use substr() function to
extract the relevant characters of the first_day_of_month
column, which is a string that contains the date in the format
“YYYY-MM-DD”. Then, as.integer() function
is used to convert the extracted year and month values from character
strings to integers.
# Add year, month and year_month columns to train_df
train_df$year <- as.integer(substr(train_df$first_day_of_month, 1, 4))
train_df$month <- as.integer(substr(train_df$first_day_of_month, 6, 7))
train_df$year_month <- substr(train_df$first_day_of_month, 1, 7)
str(train_df)## 'data.frame': 122265 obs. of 10 variables:
## $ row_id : chr "1001_2019-08-01" "1001_2019-09-01" "1001_2019-10-01" "1001_2019-11-01" ...
## $ cfips : int 1001 1001 1001 1001 1001 1001 1001 1001 1001 1001 ...
## $ county : chr "Autauga County" "Autauga County" "Autauga County" "Autauga County" ...
## $ state : chr "Alabama" "Alabama" "Alabama" "Alabama" ...
## $ first_day_of_month : Date, format: "2019-08-01" "2019-09-01" ...
## $ microbusiness_density: num 3.01 2.88 3.06 2.99 2.99 ...
## $ active : int 1249 1198 1269 1243 1243 1242 1217 1227 1255 1257 ...
## $ year : int 2019 2019 2019 2019 2019 2020 2020 2020 2020 2020 ...
## $ month : int 8 9 10 11 12 1 2 3 4 5 ...
## $ year_month : chr "2019-08" "2019-09" "2019-10" "2019-11" ...# Add year, month and year_month columns to test_df
test_df$year <- as.integer(substr(test_df$first_day_of_month, 1, 4))
test_df$month <- as.integer(substr(test_df$first_day_of_month, 6, 7))
test_df$year_month <- substr(test_df$first_day_of_month, 1, 7)3.6. Merging the train and imputed_data datasets
The merging process is challenging because all data fields provided
in the imputed_data (formerly
census_df) dataframe have a two-year lag to match the
data in the train_df dataframe. Also, the data provided
in the imputed_data is on a yearly basis, but the data
in the train_df dataframe is on a monthly basis. To
merge these two dataframes, it is assumed that the yearly data provided
is valid for all the months of the corresponding year. For example, data
provided in the pct_bb_2017 is valid for all the months of
2019 in the train_df.
# Set variables of interest
vars <- c("pct_bb", "pct_college", "pct_foreign_born", "pct_it_workers", "median_hh_inc")
# Loop through variables and merge with train_df
merged_df <- train_df
for (var in vars) {
# Select columns and pivot longer
merged_df <- imputed_data %>%
select(cfips, paste0(var, "_2017"):paste0(var, "_2020")) %>%
pivot_longer(cols = starts_with(var),
names_to = "year",
values_to = var) %>%
# Modify year and month columns
mutate(year = as.integer(str_sub(year, -4)) + 2) %>%
uncount(12, .id = "month") %>%
mutate(month = month) %>%
# Merge with merged_df
merge(merged_df, by = c("cfips", "year", "month"), all.x = TRUE) %>%
arrange(cfips, row_id)
}
merged_df <- merged_df %>%
select(row_id, cfips, county, state, first_day_of_month, microbusiness_density, active, year_month, year, month, pct_bb, pct_college, pct_foreign_born, pct_it_workers, median_hh_inc)
merged_test <- test_df
for (var in vars) {
# Select columns and pivot longer
merged_test <- imputed_data %>%
select(cfips, paste0(var, "_2020"):paste0(var, "_2021")) %>%
pivot_longer(cols = starts_with(var),
names_to = "year",
values_to = var) %>%
# Modify year and month columns
mutate(year = as.integer(str_sub(year, -4)) + 2) %>%
uncount(12, .id = "month") %>%
mutate(month = month) %>%
# Merge with merged_df
merge(merged_test, by = c("cfips", "year", "month"), all.x = TRUE) %>%
arrange(cfips, row_id)
}
merged_test <- merged_test %>%
select(row_id, cfips, first_day_of_month, year_month, year, month, pct_bb, pct_college, pct_foreign_born, pct_it_workers, median_hh_inc)colSums(is.na(merged_df))## row_id cfips county
## 28551 0 28551
## state first_day_of_month microbusiness_density
## 28551 28551 28551
## active year_month year
## 28551 28551 0
## month pct_bb pct_college
## 0 0 0
## pct_foreign_born pct_it_workers median_hh_inc
## 0 0 0colSums(is.na(merged_test))## row_id cfips first_day_of_month year_month
## 50328 0 50328 50328
## year month pct_bb pct_college
## 0 0 0 0
## pct_foreign_born pct_it_workers median_hh_inc
## 0 0 0Since the data from 1/2019 to 7/2019 and 11/2022 to 12/2022 is not available in train_df merging the data has created NA values in merged_df for those months. Now we have to remove the rows with missing values.
# remove NA values created in merged_df
merged_df <- merged_df %>%
na.omit(merged_df)
merged_test <- merged_test %>%
na.omit(merged_test)colSums(is.na(merged_df))## row_id cfips county
## 0 0 0
## state first_day_of_month microbusiness_density
## 0 0 0
## active year_month year
## 0 0 0
## month pct_bb pct_college
## 0 0 0
## pct_foreign_born pct_it_workers median_hh_inc
## 0 0 0colSums(is.na(merged_test))## row_id cfips first_day_of_month year_month
## 0 0 0 0
## year month pct_bb pct_college
## 0 0 0 0
## pct_foreign_born pct_it_workers median_hh_inc
## 0 0 0summary(merged_df)## row_id cfips county state
## Length:122265 Min. : 1001 Length:122265 Length:122265
## Class :character 1st Qu.:18177 Class :character Class :character
## Mode :character Median :29173 Mode :character Mode :character
## Mean :30376
## 3rd Qu.:45077
## Max. :56045
## first_day_of_month microbusiness_density active
## Min. :2019-08-01 Min. : 0.000 Min. : 0
## 1st Qu.:2020-05-01 1st Qu.: 1.639 1st Qu.: 145
## Median :2021-03-01 Median : 2.587 Median : 488
## Mean :2021-03-01 Mean : 3.818 Mean : 6443
## 3rd Qu.:2022-01-01 3rd Qu.: 4.519 3rd Qu.: 2124
## Max. :2022-10-01 Max. :284.340 Max. :1167744
## year_month year month pct_bb
## Length:122265 Min. :2019 Min. : 1.000 Min. :24.50
## Class :character 1st Qu.:2020 1st Qu.: 4.000 1st Qu.:69.30
## Mode :character Median :2021 Median : 7.000 Median :75.80
## Mean :2021 Mean : 6.692 Mean :74.69
## 3rd Qu.:2022 3rd Qu.:10.000 3rd Qu.:81.20
## Max. :2022 Max. :12.000 Max. :97.10
## pct_college pct_foreign_born pct_it_workers median_hh_inc
## Min. : 0.00 Min. : 0.000 Min. : 0.000 Min. : 19264
## 1st Qu.:10.10 1st Qu.: 1.400 1st Qu.: 0.700 1st Qu.: 43505
## Median :13.20 Median : 2.700 Median : 1.200 Median : 51094
## Mean :14.22 Mean : 4.745 Mean : 1.356 Mean : 52830
## 3rd Qu.:17.30 3rd Qu.: 5.700 3rd Qu.: 1.800 3rd Qu.: 59230
## Max. :48.00 Max. :54.000 Max. :17.400 Max. :1471113.7. Data Visualization
The main feature in this project is
microbusiness_density provided in the
merged_df. Also, the number of active microbusinesses
is provided in the active column.
3.7.1. Overall Microbusiness Density and Count
First, we will plot overall microbusiness density and count of active microbusiness in the United States:
# Create plots
p1 <- merged_df %>%
# Group merged_df by year_month
group_by(year_month) %>%
# calculate the mean value of microbusiness_density for each group
summarise(mean_microbusiness_density = mean(microbusiness_density)) %>%
ggplot(aes(x = year_month, y = mean_microbusiness_density, group = 1)) +
geom_line() +
labs(title = "Overall Microbusiness Density Average",
x = "Year-Month",
y = "Average Microbusiness Density") +
theme(axis.text.x = element_text(angle = 45, hjust = 1))
p2 <- merged_df %>%
group_by(year_month) %>%
summarize(avg_active = mean(active)) %>%
ggplot(aes(x = year_month, y = avg_active)) +
geom_line(group = 1) +
labs(title = "Overall Active Microbusiness Count",
x = "Year-Month",
y = "Active") +
theme(axis.text.x = element_text(angle = 45, hjust = 1))
# Display the plots
grid.arrange(p1, p2, nrow = 2)
As expected, these two graphs show almost similar behavior. If we ignore the slight fluctuations of the two graphs, the general microbusiness density and count are growing over the whole time frame.
# Create plots
p1 <- merged_df %>%
# Group merged_df by year_month
group_by(year_month) %>%
# calculate the median value of microbusiness_density for each group
summarise(median_microbusiness_density = median(microbusiness_density)) %>%
ggplot(aes(x = year_month, y = median_microbusiness_density, group = 1)) +
geom_line() +
labs(title = "Overall Microbusiness Density Median",
x = "Year-Month",
y = "Microbusiness Density Median") +
theme(axis.text.x = element_text(angle = 45, hjust = 1))
p2 <- merged_df %>%
group_by(year_month) %>%
summarize(median_active = median(active)) %>%
ggplot(aes(x = year_month, y = median_active)) +
geom_line(group = 1) +
labs(title = "Overall Active Microbusiness Count Median",
x = "Year-Month",
y = "Active Median") +
theme(axis.text.x = element_text(angle = 45, hjust = 1))
# Display the plots
grid.arrange(p1, p2, nrow = 2)
Then, we will examine the behavior of these two variables (microbusiness density and active) while grouping the data by month and year:
# Group merged_df by year and calculate the mean value of microbusiness_density and active for each group
merged_df_mean_year <- merged_df %>%
group_by(year) %>%
summarize(avg_microbusiness_density = mean(microbusiness_density),
avg_active = mean(active))
# Group merged_df by month and calculate the mean value of the microbusiness_density for each group
merged_df_mean_month <- merged_df %>%
group_by(month) %>%
summarize(avg_microbusiness_density = mean(microbusiness_density),
avg_active = mean(active))
# Plot the monthly mean values for microbusiness density
p1 <-
ggplot(merged_df_mean_month, aes(x = month, y = avg_microbusiness_density)) +
geom_line() +
ggtitle("Average Monthly Microbusiness Density") +
xlab("Month") +
ylab("Avg Microbusiness Density") +
theme(axis.text.x = element_text(angle = 45, hjust = 1))
# Plot the yearly mean values for microbusiness density
p2 <-
ggplot(merged_df_mean_year, aes(x = year, y = avg_microbusiness_density)) +
geom_line() +
ggtitle("Average Yearly Microbusiness Density") +
xlab("Year") +
ylab("Avg Microbusiness Density") +
theme(axis.text.x = element_text(angle = 45, hjust = 1))
# Plot the monthly mean values for active
p3 <-
ggplot(merged_df_mean_month, aes(x = month, y = avg_active)) +
geom_line() +
ggtitle("Average Monthly Active Microbusiness Count") +
xlab("Month") +
ylab("Avg Microbusiness Count") +
theme(axis.text.x = element_text(angle = 45, hjust = 1))
# Plot the yearly mean values for active
p4 <-
ggplot(merged_df_mean_year, aes(x = year, y = avg_active)) +
geom_line() +
ggtitle("Average Yearly Active Microbusiness Count") +
xlab("Year") +
ylab("Avg Microbusiness Count") +
theme(axis.text.x = element_text(angle = 45, hjust = 1))
# Display the plots side by side
grid.arrange(p2, p1, p4, p3, nrow = 2, ncol = 2)
The left plots show that the average microbusiness density has increased slightly over the years, starting at approximately 3.73 in 2019 and reaching 3.94 in 2022. On the other hand, the average active count has also increased, starting at approximately 6274 in 2019 and reaching 6679 in 2022. In comparison, the right plots show fluctuations in the monthly averages for both variables. Generally, it follows a slightly upward trend over the year, with some peak values observed in July and October for the microbusiness density and active count, respectively. These peak values may represent seasonal variations, indicating that microbusinesses are more active during certain months. Overall, the plot shows some correlation between the monthly average values of microbusiness_density and active count, indicating that common factors may influence both variables.
# Create a grid of box plots
ggplot(merged_df, aes(x=year_month, y=microbusiness_density)) +
geom_boxplot() +
labs(x="Year-Month", y="Microbusiness Density") +
ggtitle("Overall Microbusiness Density Average") +
theme(axis.text.x = element_text(angle = 45, hjust = 1))
Above plot is not very informative because the small values are obscured by the larger ones. Therefore, using a logarithmic scale on the Y-axis can help to reduce this distortion and provide a more informative visualization of the data.
# Create a grid of box plots
ggplot(merged_df, aes(x=year_month, y=microbusiness_density)) +
geom_boxplot() +
scale_y_log10() +
labs(x="Year-Month", y="Microbusiness Density") +
ggtitle("Overall Microbusiness Density Average") +
theme(axis.text.x = element_text(angle = 45, hjust = 1))
3.7.2. Economic Regional Divisions
The Bureau of Economic Analysis (BEA) divides the United States into eight distinct economic regions1.
These regions are based on similarities in economic characteristics such as industry composition, income levels, and employment patterns. The eight regions are:
New England: Connecticut, Maine, Massachusetts, New Hampshire, Rhode Island, and Vermont.
The economy in this region is largely based on manufacturing, healthcare, education, and finance.
Mideast: Delaware, Maryland, New Jersey, New York, Pennsylvania, and the District of Columbia.
The region has a diverse economy, with a mix of manufacturing, finance, healthcare, and professional services.
Great Lakes: Illinois, Indiana, Michigan, Ohio, and Wisconsin.
The region has a strong manufacturing base, particularly in the automotive industry, and also has a significant healthcare sector.
Plains: Iowa, Kansas, Minnesota, Missouri, Nebraska, North Dakota, and South Dakota.
Agriculture and energy production are major industries in this region, along with manufacturing and healthcare.
Southeast: Alabama, Arkansas, Florida, Georgia, Kentucky, Louisiana, Mississippi, North Carolina, South Carolina, Tennessee, Virginia, and West Virginia.
The Southeast has a diverse economy, with significant industries in healthcare, finance, and manufacturing, as well as tourism and agriculture.
Southwest: Arizona, New Mexico, Oklahoma, and Texas.
The region has a strong energy sector, particularly in oil and gas production, and also has significant industries in manufacturing, healthcare, and finance.
Rocky Mountain: Colorado, Idaho, Montana, Utah, and Wyoming.
The region is known for its natural resources, particularly in mining and energy production, as well as tourism, healthcare, and manufacturing.
Far West: Alaska, California, Hawaii, Nevada, Oregon, and Washington.
This region has a diverse economy, with significant industries in technology, finance, healthcare, and manufacturing, as well as tourism and agriculture.
To draw the map for the BEA regions, first, we need to convert state
and county columns in merged_df to lowercase letters.
Merging two dataframes will cause problems because the data from
map_data() will be in lowercase
letters.
# Convert state and county columns in merged_df to lowercase
merged_df <- merged_df %>%
mutate(state = tolower(state)) %>%
mutate(county = tolower(county))Then, we’ll create a new column in merged_df named
region and assign region values based on state
column:
# Create a new column named region and initialize all values as NA
merged_df$region <- NA
# Assign region values based on state column
for (i in 1:nrow(merged_df)) {
if (merged_df$state[i] %in% c("connecticut", "maine", "massachusetts", "new hampshire", "rhode island", "vermont")) {
merged_df$region[i] <- "new england"
} else if (merged_df$state[i] %in% c("delaware", "maryland", "new jersey", "new york", "pennsylvania", "district of columbia")) {
merged_df$region[i] <- "mideast"
} else if (merged_df$state[i] %in% c("illinois", "indiana", "michigan", "ohio", "wisconsin")) {
merged_df$region[i] <- "great lakes"
} else if (merged_df$state[i] %in% c("iowa", "kansas", "minnesota", "missouri", "nebraska", "north dakota", "south dakota")) {
merged_df$region[i] <- "plains"
} else if (merged_df$state[i] %in% c("alabama", "arkansas", "florida", "georgia", "kentucky", "louisiana", "mississippi", "north carolina", "south carolina", "tennessee", "virginia", "west virginia")) {
merged_df$region[i] <- "southeast"
} else if (merged_df$state[i] %in% c("arizona", "new mexico", "oklahoma", "texas")) {
merged_df$region[i] <- "southwest"
} else if (merged_df$state[i] %in% c("colorado", "idaho", "montana", "utah", "wyoming")) {
merged_df$region[i] <- "rocky mountain"
} else if (merged_df$state[i] %in% c("alaska", "california", "hawaii", "nevada", "oregon", "washington")) {
merged_df$region[i] <- "far west"
} else {
merged_df$region[i] <- "other"
}
}# Print all the unique values in the region column
unique(merged_df$region)## [1] "southeast" "far west" "southwest" "rocky mountain"
## [5] "new england" "mideast" "great lakes" "plains"Now that the data in the dataframe matches the
map_data() output, we appoint each state
to the region it belongs to and then use
ggplot() to draw the map:
# Get the map of the United States
us_map <- map_data("state")
# Create a lookup table for state abbreviations and their corresponding full names
state_names <- data.frame(state = state.abb, name = tolower(state.name))
# Map the regions to the states
region_map <- us_map %>%
#left_join(state_names, by = c("region" = "state")) %>%
left_join(state_names, by = c("region" = "name")) %>%
# merge(us_map, state_names, by.x=c("region"), by.y=c("name")) %>%
mutate(region =
ifelse(region %in% c("connecticut", "maine", "massachusetts", "new hampshire", "rhode island", "vermont"), "New England",
ifelse(region %in% c("delaware", "maryland", "new jersey", "new york", "pennsylvania", "district of columbia"), "Mideast",
ifelse(region %in% c("illinois", "indiana", "michigan", "ohio", "wisconsin"), "Great Lakes",
ifelse(region %in% c("iowa", "kansas", "minnesota", "missouri", "nebraska", "north dakota", "south dakota"), "Plains",
ifelse(region %in% c("alabama", "arkansas", "florida", "georgia", "kentucky", "louisiana", "mississippi", "north carolina", "south carolina", "tennessee", "virginia", "west virginia"), "Southeast",
ifelse(region %in% c("arizona", "new mexico", "oklahoma", "texas"), "Southwest",
ifelse(region %in% c("colorado", "idaho", "montana", "utah", "wyoming"), "Rocky Mountain",
ifelse(region %in% c("alaska", "california", "hawaii", "nevada", "oregon", "washington"), "Far West", NA
)))))))))
# Summarize the data to get the center coordinates of each state
#state_centers <- region_map %>%
# group_by(state) %>%
# summarise(long = mean(long), lat = mean(lat))
# add labels
states <- aggregate(cbind(long, lat) ~ region, data=us_map,
FUN=function(x)mean(range(x)))
states$group <- c("AL", "AR", "AZ", "CA", "CO", "CT", "DE", "DC", "FL", "GA", "IA",
"ID", "IL", "IN", "KS", "KY", "LA", "MA", "MD", "ME", "MI", "MN",
"MO", "MS", "MT", "NC", "ND", "NE", "NH", "NJ", "NM", "NV", "NY",
"OH", "OK", "OR", "PA", "RI", "SC", "SD", "TN", "TX", "UT", "VA",
"VT", "WA", "WI", "WV", "WY")
# names(states)[names(states) == "region"] <- "group"
#Plot the map
ggplot(region_map, aes(x = long, y = lat, group = group, fill = region)) +
geom_polygon(color = "black", show.legend = TRUE) +
# geom_text(aes(label = state), data = region_map, size = 3, vjust = 2, hjust = 2) +
# geom_text(aes(label = state), data = state_centers, size = 2, vjust = 2, hjust = 2) +
geom_text(data = states, aes(long, lat, label = group), size = 2.5, inherit.aes = FALSE, color = "white", fontface = "bold") +
# scale_fill_gradient(low = "white", high = "darkred") +
# scale_fill_manual(values = viridis(n = 60), na.value = "gray") +
labs(title = "Bureau of Economic Analysis Regional Divisions Map", fill = "Region") +
# geom_text(aes(x = long, y = lat, label = state), data = state_centers, size = 3, color = "white") +
theme_void() +
theme(panel.background = element_rect(fill = "gray75", color = NA))
# Group merged_df by region and calculate average microbusiness density
merged_df %>%
group_by(region) %>%
summarize(avg_density = mean(microbusiness_density)) %>%
# Create bar plot of average density by region
ggplot(aes(x = region, y = avg_density)) +
geom_bar(stat = "identity") +
# Add plot title and axis labels
labs(title = "Average Microbusiness Density Per Region",
x = "Region", y = "Avg Density") +
# Apply a black and white theme to the plot
theme_bw()
According to the above plot New England has the highest average microbusiness density, followed by Farwest and Rocky Mountain respectively, with a tiny difference, valuing more than 6.75. In contrast, plains has the lowest average microbusiness density, followed by Southeast and Southwest, all valued under 3.25. We can use a choropleth map to get a better view on the above information.
# choropleth map
# Group merged_df by region and calculate average microbusiness density
avg_density <- merged_df %>%
group_by(region) %>%
summarize(avg_density = mean(microbusiness_density))
# Create a lookup table for state abbreviations and their corresponding full names
state_names <- data.frame(state = state.abb, name = tolower(state.name))
# Lowercase region column of region_map
region_map <- region_map %>%
mutate(region = tolower(region))
# Merge the average density data with the region_map data
plot_data <- merge(region_map, avg_density, by = "region") %>%
arrange(order)
# Coordinates of the center of regions
bea_regions <- data.frame(
group = c("New England", "Mideast", "Great Lakes", "Plains",
"Southeast", "Southwest", "Rocky Mountain", "Far West"),
x = c(-71.8, -76.9, -86.6, -98.5, -82.4, -106.4, -111.1, -119.8),
y = c(42.2, 39, 43.4, 39.8, 32.6, 34.3, 44.4, 38.4)
)
# Create the plot
ggplot(plot_data, aes(x = long, y = lat, group = group, fill = avg_density)) +
geom_polygon(color = "black") +
geom_label(data = bea_regions,
aes(x = x, y = y, label = group),
size = 3, fontface = "bold",
label.padding = unit(0.2, "lines"),
label.size = 0.2,
fill = "gray75", color = "black") +
scale_fill_gradient(low = "gray85", high = "darkred") +
# scale_fill_viridis(name = "Avg Density", na.value = "gray") +
labs(title = "Average Microbusiness Density Per Region", fill = "Avg Density") +
theme_void() 
# theme(panel.background = element_rect(fill = "gray90", color = NA))Although, we can only see only one parameter on above map. To have a
better look on the distribution, central tendency, spread, and
variability of the microbusiness_density variable, we can
use boxplots.
# Aggregate data by region
df_by_region <- aggregate(microbusiness_density ~ region, merged_df, median)
# Create boxplot
ggplot(merged_df, aes(x = region, y = microbusiness_density)) +
geom_boxplot() +
labs(x = "Region", y = "Microbusiness Density") +
# Arrange plots in grid
facet_wrap(~ region, scales = "free", nrow = 2)
Above plots are not very informative because the small values are obscured by the larger ones. Therefore, using a logarithmic scale on the Y-axis can help to reduce this distortion and provide a more informative visualization of the data.
# Create a grid of box plots
ggplot(merged_df, aes(x=region, y=microbusiness_density)) +
geom_boxplot() +
scale_y_log10() +
labs(x="Region", y="Microbusiness Density") +
ggtitle("Microbusiness Density by Region")
These boxplots are more informative, because using a logarithmic scale on the Y-axis helps to better reveal the differences and similarities between regions that helps to highlight any potential patterns or trends in the data. Some of the points that can be inferred from this boxplot include:
All regions have at least some microbusiness activity. Because minimum microbusiness density is greater than 0 in all regions.
The median microbusiness density is highest in the New England region, followed by the Far West and the Mideast regions.
The 3rd quartile microbusiness density is highest in the Rocky Mountain region, followed by the New England and the Far West regions.
The maximum microbusiness density is highest in the Plains region, followed by the Rocky Mountain and the Far West regions.
The mean microbusiness density is highest in the New England region, followed by the Far West and the Rocky Mountain regions.
The interquartile range (IQR = the difference between the 1st and 3rd quartiles) of microbusiness density is widest in the Rocky Mountain region, indicating that there is a greater range of microbusiness density in that region. In contrast, the IQR is narrowest in the Plains region.
# by(merged_df$microbusiness_density, merged_df$region, summary)# Aggregate microbusiness density by state
state_avg <- aggregate(microbusiness_density ~ state, data = merged_df, FUN = mean)
# Load US map data
us_map <- map_data("state")
# Merge state_avg with us_map based on region and state
map_data <- merge(us_map, state_avg, by.x = "region", by.y = "state")
# Create a heatmap of microbusiness density by state
ggplot(map_data, aes(x = long, y = lat, group = group, fill = microbusiness_density)) +
geom_polygon() +
scale_fill_gradient(low = "white", high = "darkgreen") +
coord_map() +
labs(title = "Average Microbusiness Density per State", fill = "Density") +
theme_void() +
theme(panel.background = element_rect(fill = "lightblue", color = NA))
# Create a grid of box plots
ggplot(merged_df, aes(x=state, y=microbusiness_density)) +
geom_boxplot(colour = "darkblue", outlier.colour = "pink") +
scale_y_log10() +
labs(x="State", y="Microbusiness Density") +
ggtitle("Microbusiness Density by State") +
theme_classic() +
theme(axis.text.x = element_text(angle = 90, hjust = 1, vjust = 0.3))
# {r fig.width = 10 ,fig.height = 12, out.width='100%', fig.align='center'}
# Aggregate microbusiness density by county
#county_avg <- merged_df %>%
# group_by(cfips, county) %>%
# summarise(microbusiness_density = mean(microbusiness_density))
county_avg <- aggregate(microbusiness_density ~ county + state, data = merged_df, FUN = mean)
# Get rid of county, city, and parish in the end of county names
county_avg$county <- gsub(" county", "", county_avg$county)
county_avg$county <- gsub(" city", "", county_avg$county)
county_avg$county <- gsub(" parish", "", county_avg$county)
# Load US county map data
us_map <- map_data("county")
# Merge county_avg with us_map based on region and county
map_data <- merge(us_map, county_avg, by.x = c("subregion", "region"), by.y = c("county", "state")) %>%
arrange(order)
# Create a heatmap of microbusiness density by county using ggplot2
ggplot(map_data, aes(x = long, y = lat, group = group, fill = microbusiness_density)) +
geom_polygon() +
scale_fill_gradient(low = "lightblue", high = "navyblue") +
coord_map() +
labs(title = "Average Microbusiness Density per County", fill = "Density") +
theme_void() +
theme(panel.background = element_rect(fill = "gray85", color = NA))
str(merged_df)## 'data.frame': 122265 obs. of 16 variables:
## $ row_id : chr "1001_2019-08-01" "1001_2019-09-01" "1001_2019-10-01" "1001_2019-11-01" ...
## $ cfips : int 1001 1001 1001 1001 1001 1001 1001 1001 1001 1001 ...
## $ county : chr "autauga county" "autauga county" "autauga county" "autauga county" ...
## $ state : chr "alabama" "alabama" "alabama" "alabama" ...
## $ first_day_of_month : Date, format: "2019-08-01" "2019-09-01" ...
## $ microbusiness_density: num 3.01 2.88 3.06 2.99 2.99 ...
## $ active : int 1249 1198 1269 1243 1243 1242 1217 1227 1255 1257 ...
## $ year_month : chr "2019-08" "2019-09" "2019-10" "2019-11" ...
## $ year : num 2019 2019 2019 2019 2019 ...
## $ month : int 8 9 10 11 12 1 2 3 4 5 ...
## $ pct_bb : num 76.6 76.6 76.6 76.6 76.6 78.9 78.9 78.9 78.9 78.9 ...
## $ pct_college : num 14.5 14.5 14.5 14.5 14.5 15.9 15.9 15.9 15.9 15.9 ...
## $ pct_foreign_born : num 2.1 2.1 2.1 2.1 2.1 2 2 2 2 2 ...
## $ pct_it_workers : num 1.3 1.3 1.3 1.3 1.3 1.1 1.1 1.1 1.1 1.1 ...
## $ median_hh_inc : num 55317 55317 55317 55317 55317 ...
## $ region : chr "southeast" "southeast" "southeast" "southeast" ...
## - attr(*, "na.action")= 'omit' Named int [1:28551] 40 41 42 43 44 45 46 47 48 88 ...
## ..- attr(*, "names")= chr [1:28551] "40" "41" "42" "43" ...Boxplots are a visualization tool that provide insights into the central tendency and spread of a dataset, as well as identify outliers and skewness. They are useful for detecting anomalies and comparing variable distributions in a dataset, providing valuable insights into data distribution for exploratory data analysis.
ggplot(merged_df, aes(y = microbusiness_density)) +
# ggplot(merged_df, aes(x=region, y=microbusiness_density)) +
geom_boxplot(colour = "blue") +
scale_y_log10() +
labs(y="Microbusiness Density") +
ggtitle("Microbusiness Density") +
theme_classic()
# Create a grid of box plots
par(mfrow=c(3,2))
p1 <- ggplot(merged_df, aes(x=region, y=median_hh_inc)) +
geom_boxplot(outlier.colour = "orange") +
scale_y_log10() +
labs(x="Region", y="Median Household Income") +
ggtitle("Median Household Income by Region") +
theme_classic() +
theme(axis.text.x = element_text(angle = 45, hjust = 1))
p2 <- ggplot(merged_df, aes(x=region, y=pct_college)) +
geom_boxplot(outlier.colour = "orange") +
scale_y_log10() +
labs(x="Region", y="Percentage with College Education") +
ggtitle("Percentage with College Education by Region") +
theme_classic() +
theme(axis.text.x = element_text(angle = 45, hjust = 1))
p3 <- ggplot(merged_df, aes(x=region, y=pct_foreign_born)) +
geom_boxplot(outlier.colour = "orange") +
scale_y_log10() +
labs(x="Region", y="Percentage of Foreign-born Residents") +
ggtitle("Percentage of Foreign-born Residents by Region") +
theme_classic() +
theme(axis.text.x = element_text(angle = 45, hjust = 1))
p4 <- ggplot(merged_df, aes(x=region, y=pct_it_workers)) +
geom_boxplot(outlier.colour = "orange") +
scale_y_log10() +
labs(x="Region", y="Percentage of IT Workers") +
ggtitle("Percentage of IT Workers by Region") +
theme_classic() +
theme(axis.text.x = element_text(angle = 45, hjust = 1))
p5 <- ggplot(merged_df, aes(x=region, y=pct_bb)) +
geom_boxplot(outlier.colour = "orange") +
scale_y_log10() +
labs(x="Region", y="Percentage of Broadband Access") +
ggtitle("Percentage of Broadband Access by Region") +
theme_classic() +
theme(axis.text.x = element_text(angle = 45, hjust = 1))
grid.arrange(p1, p2, p3, p4, p5, nrow = 5)
# Create a grid of box plots
p1 <- ggplot(merged_df, aes(x=state, y=median_hh_inc)) +
geom_boxplot(outlier.colour = "orange") +
scale_y_log10() +
labs(x="State", y="Median Household Income") +
ggtitle("Median Household Income by State") +
theme_classic() +
theme(axis.text.x = element_text(angle = 90, hjust = 1, vjust = 0.3))
p2 <- ggplot(merged_df, aes(x=state, y=pct_college)) +
geom_boxplot(outlier.colour = "orange") +
scale_y_log10() +
labs(x="State", y="Percentage with College Education") +
ggtitle("Percentage with College Education by State") +
theme_classic() +
theme(axis.text.x = element_text(angle = 90, hjust = 1, vjust = 0.3))
p3 <- ggplot(merged_df, aes(x=state, y=pct_foreign_born)) +
geom_boxplot(outlier.colour = "orange") +
scale_y_log10() +
labs(x="State", y="Percentage of Foreign-born Residents") +
ggtitle("Percentage of Foreign-born Residents by State") +
theme_classic() +
theme(axis.text.x = element_text(angle = 90, hjust = 1, vjust = 0.3))
p4 <- ggplot(merged_df, aes(x=state, y=pct_it_workers)) +
geom_boxplot(outlier.colour = "orange") +
scale_y_log10() +
labs(x="State", y="Percentage of IT Workers") +
ggtitle("Percentage of IT Workers by State") +
theme_classic() +
theme(axis.text.x = element_text(angle = 90, hjust = 1, vjust = 0.3))
p5 <- ggplot(merged_df, aes(x=state, y=pct_bb)) +
geom_boxplot(outlier.colour = "orange") +
scale_y_log10() +
labs(x="State", y="Percentage of Broadband Access") +
ggtitle("Percentage of Broadband Access by State") +
theme_classic() +
theme(axis.text.x = element_text(angle = 90, hjust = 1, vjust = 0.3))
grid.arrange(p1, p2, p3, p4, p5, nrow = 5)
# choropleth map with 5 variables
# Group merged_df by region and calculate average variables
avg_variables <- merged_df %>%
group_by(region) %>%
summarize(avg_pct_bb = mean(pct_bb),
avg_pct_college = mean(pct_college),
avg_pct_foreign_born = mean(pct_foreign_born),
avg_pct_it_workers = mean(pct_it_workers),
avg_median_hh_inc = mean(median_hh_inc))
# Create a lookup table for state abbreviations and their corresponding full names
state_names <- data.frame(state = state.abb, name = tolower(state.name))
# Lowercase region column of region_map
region_map <- region_map %>%
mutate(region = tolower(region))
# Merge the average density data with the region_map data
plot_data <- merge(region_map, avg_variables, by = "region") %>%
arrange(order)
# Coordinates of the center of regions
bea_regions <- data.frame(
group = c("New England", "Mideast", "Great Lakes", "Plains",
"Southeast", "Southwest", "Rocky Mountain", "Far West"),
x = c(-71.8, -76.9, -86.6, -98.5, -82.4, -106.4, -111.1, -119.8),
y = c(42.2, 39, 43.4, 39.8, 32.6, 34.3, 44.4, 38.4)
)
# Create the plot with a grid of 5 rows and 1 column
p1 <- ggplot(plot_data, aes(x = long, y = lat, group = group, fill = avg_pct_bb)) +
geom_polygon(color = "black") +
geom_label(data = bea_regions,
aes(x = x, y = y, label = group),
size = 3, fontface = "bold",
label.padding = unit(0.2, "lines"),
label.size = 0.2,
fill = "gray75", color = "black") +
scale_fill_gradient(low = "gray85", high = "darkred") +
labs(title = "Average Percent of Broadband Access Per Region", fill = "Avg Density") +
theme_void()
p2 <- ggplot(plot_data, aes(x = long, y = lat, group = group, fill = avg_pct_college)) +
geom_polygon(color = "black") +
geom_label(data = bea_regions,
aes(x = x, y = y, label = group),
size = 3, fontface = "bold",
label.padding = unit(0.2, "lines"),
label.size = 0.2,
fill = "gray75", color = "black") +
scale_fill_gradient(low = "gray85", high = "darkred") +
labs(title = "Average Percent of College Graduates Per Region", fill = "Avg Percent") +
theme_void()
p3 <- ggplot(plot_data, aes(x = long, y = lat, group = group, fill = avg_pct_foreign_born)) +
geom_polygon(color = "black") +
geom_label(data = bea_regions,
aes(x = x, y = y, label = group),
size = 3, fontface = "bold",
label.padding = unit(0.2, "lines"),
label.size = 0.2,
fill = "gray75", color = "black") +
scale_fill_gradient(low = "gray85", high = "darkred") +
labs(title = "Average Percent of Foreign-Born Population Per Region", fill = "Avg Percent") +
theme_void()
p4 <- ggplot(plot_data, aes(x = long, y = lat, group = group, fill = avg_pct_it_workers)) +
geom_polygon(color = "black") +
geom_label(data = bea_regions,
aes(x = x, y = y, label = group),
size = 3, fontface = "bold",
label.padding = unit(0.2, "lines"),
label.size = 0.2,
fill = "gray75", color = "black") +
scale_fill_gradient(low = "gray85", high = "darkred") +
labs(title = "Average Percent of IT Workers Per Region", fill = "Avg Percent") +
theme_void()
p5 <- ggplot(plot_data, aes(x = long, y = lat, group = group, fill = avg_median_hh_inc)) +
geom_polygon(color = "black") +
geom_label(data = bea_regions,
aes(x = x, y = y, label = group),
size = 3, fontface = "bold",
label.padding = unit(0.2, "lines"),
label.size = 0.2,
fill = "gray75", color = "black") +
scale_fill_gradient(low = "gray85", high = "darkred") +
labs(title = "Average Median Household inc Per Region", fill = "Avg inc") +
theme_void()
grid.arrange(p1, p2, p3, p4, p5, nrow = 5)
state_avg <- aggregate(cbind(pct_bb, pct_college, pct_foreign_born, pct_it_workers, median_hh_inc) ~ state, data = merged_df, FUN = mean)
#Load US state map data
us_map <- map_data("state")
#Merge state_avg with us_map based on region and state
map_data <- merge(us_map, state_avg, by.x = c("region"), by.y = c("state")) %>%
arrange(order)
#Create a grid of heatmaps for each variable
grid_arrange_shared_legend <- function(...) {
plots <- list(...)
g <- ggplotGrob(plots[[1]] + theme(legend.position="bottom"))$grobs
legend <- g[[which(sapply(g, function(x) x$name) == "guide-box")]]
lheight <- sum(legend$height)
grid.arrange(
do.call(arrangeGrob, lapply(plots, function(x)
x + theme(legend.position="none") + theme(panel.background = element_rect(fill = "gray85", color = NA)))
),
bottom = legend,
ncol = 5,
heights = rep((unit(1, "npc") - lheight) / length(plots), length(plots))
)
}
heatmap_bb <- ggplot(map_data, aes(x = long, y = lat, group = group, fill = pct_bb)) +
geom_polygon() +
scale_fill_gradient(low = "white", high = "darkgreen") +
coord_map() +
labs(title = "Percent of Broadband Access per State", fill = "Percent") +
theme_void()
heatmap_college <-
ggplot(map_data, aes(x = long, y = lat, group = group, fill = pct_college)) +
geom_polygon() +
scale_fill_gradient(low = "white", high = "darkgreen") +
coord_map() +
labs(title = "Percent of Population with College Education per State", fill = "Percent") +
theme_void()
heatmap_foreign_born <-
ggplot(map_data, aes(x = long, y = lat, group = group, fill = pct_foreign_born)) +
geom_polygon() +
scale_fill_gradient(low = "white", high = "darkgreen") +
coord_map() +
labs(title = "Percent of Foreign-born Population per State", fill = "Percent") +
theme_void()
heatmap_it_workers <-
ggplot(map_data, aes(x = long, y = lat, group = group, fill = pct_it_workers)) +
geom_polygon() +
scale_fill_gradient(low = "white", high = "darkgreen") +
coord_map() +
labs(title = "Percent of IT Workers per State", fill = "Percent") +
theme_void()
heatmap_inc <-
ggplot(map_data, aes(x = long, y = lat, group = group, fill = median_hh_inc)) +
geom_polygon() +
scale_fill_gradient(low = "white", high = "darkgreen") +
coord_map() +
labs(title = "Median Household Income per State", fill = "Dollars") +
theme_void()
#Plot the grid of heatmaps
#grid_arrange_shared_legend(heatmap_bb, heatmap_college, heatmap_foreign_born, heatmap_it_workers, heatmap_inc)
grid.arrange(heatmap_bb, heatmap_college, heatmap_foreign_born, heatmap_it_workers, heatmap_inc, nrow = 5)
county_avg <- aggregate(cbind(pct_bb, pct_college, pct_foreign_born, pct_it_workers, median_hh_inc) ~ county + state, data = merged_df, FUN = mean)
#Get rid of county, city, and parish in the end of county names
county_avg$county <- gsub(" county", "", county_avg$county)
county_avg$county <- gsub(" city", "", county_avg$county)
county_avg$county <- gsub(" parish", "", county_avg$county)
#Load US county map data
us_map <- map_data("county")
#Merge county_avg with us_map based on region and county
map_data <- merge(us_map, county_avg, by.x = c("subregion", "region"), by.y = c("county", "state")) %>%
arrange(order)
#Create a grid of heatmaps for each variable
grid_arrange_shared_legend <- function(...) {
plots <- list(...)
g <- ggplotGrob(plots[[1]] + theme(legend.position="bottom"))$grobs
legend <- g[[which(sapply(g, function(x) x$name) == "guide-box")]]
lheight <- sum(legend$height)
grid.arrange(
do.call(arrangeGrob, lapply(plots, function(x)
x + theme(legend.position="none") + theme(panel.background = element_rect(fill = "gray85", color = NA)))
),
bottom = legend,
ncol = 5,
heights = rep((unit(1, "npc") - lheight) / length(plots), length(plots))
)
}
heatmap_bb <- ggplot(map_data, aes(x = long, y = lat, group = group, fill = pct_bb)) +
geom_polygon() +
scale_fill_gradient(low = "lightblue", high = "navyblue") +
coord_map() +
labs(title = "Percent of Broadband Access per County", fill = "Percent") +
theme_void()
heatmap_college <-
ggplot(map_data, aes(x = long, y = lat, group = group, fill = pct_college)) +
geom_polygon() +
scale_fill_gradient(low = "lightblue", high = "navyblue") +
coord_map() +
labs(title = "Percent of Population with College Education per County", fill = "Percent") +
theme_void()
heatmap_foreign_born <-
ggplot(map_data, aes(x = long, y = lat, group = group, fill = pct_foreign_born)) +
geom_polygon() +
scale_fill_gradient(low = "lightblue", high = "navyblue") +
coord_map() +
labs(title = "Percent of Foreign-born Population per County", fill = "Percent") +
theme_void()
heatmap_it_workers <-
ggplot(map_data, aes(x = long, y = lat, group = group, fill = pct_it_workers)) +
geom_polygon() +
scale_fill_gradient(low = "lightblue", high = "navyblue") +
coord_map() +
labs(title = "Percent of IT Workers per County", fill = "Percent") +
theme_void()
heatmap_inc <-
ggplot(map_data, aes(x = long, y = lat, group = group, fill = median_hh_inc)) +
geom_polygon() +
scale_fill_gradient(low = "lightblue", high = "navyblue") +
coord_map() +
labs(title = "Median Household Income per County", fill = "Dollars") +
theme_void()
#Plot the grid of heatmaps
#grid_arrange_shared_legend(heatmap_bb, heatmap_college, heatmap_foreign_born, heatmap_it_workers, heatmap_inc)
grid.arrange(heatmap_bb, heatmap_college, heatmap_foreign_born, heatmap_it_workers, heatmap_inc, nrow = 5)
par(mfrow=c(3,2)) # set plot layout to 3 rows and 2 columns
boxplot(merged_df$median_hh_inc, col = "pink", main = "Median Household Income")
boxplot(merged_df$pct_college, col = "pink", main = "Percentage with College Education")
boxplot(merged_df$pct_foreign_born, col = "pink", main = "Percentage of Foreign-born Residents")
boxplot(merged_df$pct_it_workers, col = "pink", main = "Percentage of IT Workers")
boxplot(merged_df$pct_bb, col = "pink", main = "Percentage of Broadband Access")
#boxplot(merged_df$active, col = "pink", main = "Active Microbusiness Count")
3.8. Outlier Detection
Outlier detection is an important step in data analysis, as outliers can significantly affect the results of statistical analyses. There are several methods to detect outliers depending on the distribution of the data.
The Shapiro-Wilk normality test is a statistical test used to
determine if a given dataset follows a normal distribution. We will
perform a Shapiro-Wilk normality test on a random sample of 5000
observations from the microbusiness_density column of
merged_df dataframe. To run this test we first set the
seed value using set.seed() function to a
specific random seed to ensure that the results are reproducible if the
code is run again. Then, we weill use the
shapiro.test() function to perform the
Shapiro-Wilk normality test on the sample_data object.
The function returns the test statistic (W) and the p-value. A W value
closer to 1 indicates that the data is more normally distributed, while
a W value closer to 0 indicates greater deviation from normality. If the
p-value is less than the significance level (typically 0.05), then the
null hypothesis (that the sample data is normally distributed) is
rejected in favor of the alternative hypothesis (that the sample data is
not normally distributed).
# Sample 5000 observations from microbusiness_density column
set.seed(92) # Set seed for reproducibility
sample_data <- sample(merged_df$microbusiness_density, 5000)
# Perform Shapiro-Wilk test on sample_data
shapiro.test(sample_data)##
## Shapiro-Wilk normality test
##
## data: sample_data
## W = 0.55179, p-value < 2.2e-16The test resulted in a W statistic of 0.55179 and a p-value of less than 2.2e-16. Based on the results of the Shapiro-Wilk normality test, it can be concluded that the sample_data is not normally distributed.
To have a better visual on distribution of the data we will use a
bell curve, a boxplot, and a Q-Q plot on
microbusiness_density.
# Calculate the mean and standard deviation of 'microbusiness_density'
mean_density <- mean(merged_df$microbusiness_density)
sd_density <- sd(merged_df$microbusiness_density)
# Create a range of values for the x-axis
x_values <- seq(mean_density - 3*sd_density, mean_density + 3*sd_density, length.out = 1000)
# Create a bell curve with mean and standard deviation calculated above
y_values <- dnorm(x_values, mean = mean_density, sd = sd_density)
# Combine the 'x_values' and 'y_values' into a data frame
density_df <- data.frame(x = x_values, y = y_values)
# Create a boxplot
boxplot <- ggplot(data = merged_df, aes(x = "", y = merged_df$microbusiness_density)) +
geom_boxplot(fill = "skyblue") +
scale_y_log10() +
labs(x = "", y = "Microbusiness Density (logarithmic)") +
ggtitle("Boxplot for Microbusiness Density")
# Create a Q-Q plot and add a diagonal line
qqplot <- ggplot(data = merged_df, aes(sample = microbusiness_density)) +
stat_qq() +
stat_qq_line(colour = "red") +
labs(x = "Theoretical Normal Quantiles", y = "Observed Quantiles") +
ggtitle("Q-Q Plot for Microbusiness Density")
# Create a histogram and add the bell curve
densityplot <- ggplot(data = merged_df, aes(x = microbusiness_density)) +
geom_histogram(aes(y = after_stat(density)), bins = 30, colour = "black", fill = "white") +
geom_line(data = density_df, aes(x = x, y = y), colour = "red", linewidth = 1) +
labs(x = "Microbusiness Density", y = "Density") +
ggtitle("Distribution of Microbusiness Density")
# Arrange the plots in one row using the 'grid.arrange' function from the 'gridExtra' package
grid.arrange(densityplot, boxplot, qqplot, ncol = 3, widths = c(2, 1, 2))
The above distribution plot explains that the dataset is
right-skewed. The boxplot shows some data points away from the upper
whisker; hence outliers are present in
microbusiness_density. Q-Q plot’s alignment is away from
the 45-degree angle depicting outliers in the dataset.
Since the data is right-skewed and not normally distributed, a common approach to detecting outliers is to use the interquartile range (IQR) method. Now, we have to find the boundary of minimum and maximum values, out of which data would be considered an outlier.
The decision range approach involves setting a range of values outside of which any observations are considered outliers. One common approach is to use the interquartile range (IQR) to define the decision range. The IQR is calculated as the difference between the third quartile (Q3) and the first quartile (Q1) of the data.
The decision range is then defined as the range from \(Q1 - 1.5 * IQR\) to \(Q3 + 1.5 * IQR\). Any observations that fall outside of this range are considered outliers. This method is useful for identifying potential outliers in a dataset and can help to ensure that statistical analyses are robust and accurate.
quartiles <- quantile(merged_df$microbusiness_density, probs = seq(0, 1, 0.25), na.rm = FALSE,
names = TRUE, type = 7, digits = 6)
quartiles## 0% 25% 50% 75% 100%
## 0.000000 1.639344 2.586543 4.519231 284.340030# Calculate IQR of microbusiness_density column
q <- quantile(merged_df$microbusiness_density, c(0.25, 0.75))
iqr <- q[2] - q[1]
# Calculate lower and upper bounds for outliers
lower_bound <- q[1] - 1.5*iqr
upper_bound <- q[2] + 1.5*iqr
# Count number of outliers
num_outliers <- sum(merged_df$microbusiness_density < lower_bound | merged_df$microbusiness_density > upper_bound)
# Calculate percent of outliers
percent_outliers <- num_outliers / length(merged_df$microbusiness_density) * 100
# Print results
cat("Number of outliers:", num_outliers, "\n")## Number of outliers: 8746cat("Percent of outliers:", percent_outliers, "%\n")## Percent of outliers: 7.153315 %# Create new dataframe without outliers
merged_df_new <- merged_df[merged_df$microbusiness_density >= lower_bound & merged_df$microbusiness_density <= upper_bound,]
# Print number of rows removed
cat("Number of rows removed:", nrow(merged_df) - nrow(merged_df_new), "\n")## Number of rows removed: 8746# Calculate the mean and standard deviation of 'microbusiness_density'
mean_density <- mean(merged_df_new$microbusiness_density)
sd_density <- sd(merged_df_new$microbusiness_density)
# Create a range of values for the x-axis
x_values <- seq(mean_density - 3*sd_density, mean_density + 3*sd_density, length.out = 1000)
# Create a bell curve with mean and standard deviation calculated above
y_values <- dnorm(x_values, mean = mean_density, sd = sd_density)
# Combine the 'x_values' and 'y_values' into a data frame
density_df <- data.frame(x = x_values, y = y_values)
# Create a boxplot
boxplot <- ggplot(data = merged_df_new, aes(x = "", y = merged_df_new$microbusiness_density)) +
geom_boxplot(fill = "skyblue") +
# scale_y_log10() +
labs(x = "", y = "Microbusiness Density") +
ggtitle("Boxplot for Microbusiness Density")
# Create a Q-Q plot and add a diagonal line
qqplot <- ggplot(data = merged_df_new, aes(sample = microbusiness_density)) +
stat_qq() +
stat_qq_line(colour = "red") +
labs(x = "Theoretical Normal Quantiles", y = "Observed Quantiles") +
ggtitle("Q-Q Plot for Microbusiness Density")
# Create a bell curve and add the bell curve
densityplot <- ggplot(data = merged_df_new, aes(x = microbusiness_density)) +
geom_histogram(aes(y = after_stat(density)), bins = 30, colour = "black", fill = "white") +
geom_line(data = density_df, aes(x = x, y = y), colour = "red", linewidth = 1) +
labs(x = "Microbusiness Density", y = "Density") +
ggtitle("Distribution of Microbusiness Density")
# Arrange the plots in one row
grid.arrange(densityplot, boxplot, qqplot, ncol = 3, widths = c(2, 1, 2))
# Calculate IQR of microbusiness_density column
q <- quantile(merged_df_new$microbusiness_density, c(0.25, 0.75))
iqr <- q[2] - q[1]
# Calculate lower and upper bounds for outliers
lower_bound <- q[1] - 1.5*iqr
upper_bound <- q[2] + 1.5*iqr
# Count number of outliers
num_outliers <- sum(merged_df_new$microbusiness_density < lower_bound | merged_df_new$microbusiness_density > upper_bound)
# Calculate percent of outliers
percent_outliers <- num_outliers / length(merged_df_new$microbusiness_density) * 100
# Print results
cat("Number of outliers:", num_outliers, "\n")## Number of outliers: 3946cat("Percent of outliers:", percent_outliers, "%\n")## Percent of outliers: 3.47607 %# Create new dataframe without outliers
merged_df_clean <- merged_df_new[merged_df_new$microbusiness_density >= lower_bound & merged_df_new$microbusiness_density <= upper_bound,]
# Print number of rows removed
cat("Number of rows removed:", nrow(merged_df_new) - nrow(merged_df_clean), "\n")## Number of rows removed: 3946cat("Total rows removed:", nrow(merged_df) - nrow(merged_df_clean))## Total rows removed: 12692# Calculate the mean and standard deviation of 'microbusiness_density'
mean_density <- mean(merged_df_clean$microbusiness_density)
sd_density <- sd(merged_df_clean$microbusiness_density)
# Create a range of values for the x-axis
x_values <- seq(mean_density - 3*sd_density, mean_density + 3*sd_density, length.out = 1000)
# Create a bell curve with mean and standard deviation calculated above
y_values <- dnorm(x_values, mean = mean_density, sd = sd_density)
# Combine the 'x_values' and 'y_values' into a data frame
density_df <- data.frame(x = x_values, y = y_values)
# Create a boxplot
boxplot <- ggplot(data = merged_df_clean, aes(x = "", y = merged_df_clean$microbusiness_density)) +
geom_boxplot(fill = "skyblue") +
# scale_y_log10() +
labs(x = "", y = "Microbusiness Density") +
ggtitle("Boxplot for Microbusiness Density")
# Create a Q-Q plot and add a diagonal line
qqplot <- ggplot(data = merged_df_clean, aes(sample = microbusiness_density)) +
stat_qq() +
stat_qq_line(colour = "red") +
labs(x = "Theoretical Normal Quantiles", y = "Observed Quantiles") +
ggtitle("Q-Q Plot for Microbusiness Density")
# Create a histogram and add the bell curve
densityplot <- ggplot(data = merged_df_clean, aes(x = microbusiness_density)) +
geom_histogram(aes(y = after_stat(density)), bins = 30, colour = "black", fill = "white") +
geom_line(data = density_df, aes(x = x, y = y), colour = "red", linewidth = 1) +
labs(x = "Microbusiness Density", y = "Density") +
ggtitle("Distribution of Microbusiness Density")
# Arrange the plots in one row using the 'grid.arrange' function from the 'gridExtra' package
grid.arrange(densityplot, boxplot, qqplot, ncol = 3, widths = c(2, 1, 2))
# Calculate the mean and standard deviation of 'pct_bb'
mean_pct_bb <- mean(merged_df$pct_bb)
sd_pct_bb <- sd(merged_df$pct_bb)
# Create a range of values for the x-axis
x_values <- seq(mean_pct_bb - 3*sd_pct_bb, mean_pct_bb + 3*sd_pct_bb, length.out = 1000)
# Create a bell curve with mean and standard deviation calculated above
y_values <- dnorm(x_values, mean = mean_pct_bb, sd = sd_pct_bb)
# Combine the 'x_values' and 'y_values' into a data frame
pct_bb_df <- data.frame(x = x_values, y = y_values)
# Create a boxplot
boxplot <- ggplot(data = merged_df, aes(x = "", y = merged_df$pct_bb)) +
geom_boxplot(fill = "skyblue") +
scale_y_log10() +
labs(x = "", y = "Microbusiness pct_bb (logarithmic)") +
ggtitle("Boxplot for Microbusiness pct_bb")
# Create a Q-Q plot and add a diagonal line
qqplot <- ggplot(data = merged_df, aes(sample = pct_bb)) +
stat_qq() +
stat_qq_line(colour = "red") +
labs(x = "Theoretical Normal Quantiles", y = "Observed Quantiles") +
ggtitle("Q-Q Plot for Microbusiness pct_bb")
# Create a histogram and add the bell curve
densityplot <- ggplot(data = merged_df, aes(x = pct_bb)) +
geom_histogram(aes(y = after_stat(density)), bins = 30, colour = "black", fill = "white") +
geom_line(data = pct_bb_df, aes(x = x, y = y), colour = "red", linewidth = 1) +
labs(x = "Microbusiness pct_bb", y = "pct_bb") +
ggtitle("Distribution of Microbusiness pct_bb")
# Arrange the plots in one row using the 'grid.arrange' function from the 'gridExtra' package
grid.arrange(densityplot, boxplot, qqplot, ncol = 3, widths = c(2, 1, 2))
# Specify the columns to analyze
cols_to_analyze <- c("pct_bb", "pct_college", "pct_it_workers", "pct_foreign_born", "median_hh_inc")
# Loop through each column and detect outliers using the IQR method
for (col in cols_to_analyze) {
# Calculate the interquartile range (IQR) of the column
q1 <- quantile(merged_df_new[[col]], 0.25)
q3 <- quantile(merged_df_new[[col]], 0.75)
iqr <- q3 - q1
# Calculate the upper and lower bounds for outliers
upper_bound <- q3 + (1.5 * iqr)
lower_bound <- q1 - (1.5 * iqr)
# Identify the outliers in the column
outliers <- merged_df_new[[col]][merged_df_new[[col]] > upper_bound | merged_df_new[[col]] < lower_bound]
# Print the results
# cat(paste("Outliers in", col, ":", toString(outliers), "\n"))
# Count number of outliers
num_outliers <- sum(merged_df_new[[col]] < lower_bound | merged_df_new[[col]] > upper_bound)
# Calculate percent of outliers
percent_outliers <- num_outliers / length(merged_df_new[[col]]) * 100
# Print results
cat("Number of outliers in", col,":", num_outliers, "\n")
cat("Percent of outliers in", col,":", percent_outliers, "%\n")
}## Number of outliers in pct_bb : 2507
## Percent of outliers in pct_bb : 2.208441 %
## Number of outliers in pct_college : 1428
## Percent of outliers in pct_college : 1.257939 %
## Number of outliers in pct_it_workers : 2556
## Percent of outliers in pct_it_workers : 2.251605 %
## Number of outliers in pct_foreign_born : 8329
## Percent of outliers in pct_foreign_born : 7.337098 %
## Number of outliers in median_hh_inc : 3410
## Percent of outliers in median_hh_inc : 3.003902 %# Create a copy of the original dataframe
merged_df_clean <- merged_df_new
# Loop through each column and detect outliers using the IQR method
for (col in cols_to_analyze) {
# Calculate the interquartile range (IQR) of the column
q1 <- quantile(merged_df_clean[[col]], 0.25)
q3 <- quantile(merged_df_clean[[col]], 0.75)
iqr <- q3 - q1
# Calculate the upper and lower bounds for outliers
upper_bound <- q3 + (1.5 * iqr)
lower_bound <- q1 - (1.5 * iqr)
# Identify the outliers in the column
outliers <- merged_df_clean[[col]][merged_df_clean[[col]] > upper_bound | merged_df_clean[[col]] < lower_bound]
# Remove the outliers from the dataframe
merged_df_clean <- merged_df_clean[!(merged_df_clean[[col]] %in% outliers), ]
}
# Print the dimensions of the original and cleaned dataframes
cat("Original dataframe dimensions:", nrow(merged_df_new), "\n")## Original dataframe dimensions: 113519cat("Cleaned dataframe dimensions:", nrow(merged_df_clean), "\n")## Cleaned dataframe dimensions: 97098cat("Total rows removed:", nrow(merged_df) - nrow(merged_df_clean), "\n")## Total rows removed: 25167cat("Total percent removed:", 100 * (nrow(merged_df) - nrow(merged_df_clean)) / nrow(merged_df),"%", "\n")## Total percent removed: 20.58398 %3.9. Non-Parametric Test
# Specify a list of column pairs to compare
col_pairs <- list(c("microbusiness_density", "pct_bb"), c("microbusiness_density", "pct_college"), c("microbusiness_density", "pct_foreign_born"), c("microbusiness_density", "pct_it_workers"), c("microbusiness_density", "median_hh_inc"))
# Loop through each column pair and perform the Wilcoxon signed-rank test
for (pair in col_pairs) {
test_result <- wilcox.test(merged_df_new[[pair[1]]], merged_df_new[[pair[2]]], paired = TRUE)
cat(paste("Wilcoxon signed-rank test results for", pair[1], "and", pair[2], ":\n"))
print(test_result)
cat("\n")
}## Wilcoxon signed-rank test results for microbusiness_density and pct_bb :
##
## Wilcoxon signed rank test with continuity correction
##
## data: merged_df_new[[pair[1]]] and merged_df_new[[pair[2]]]
## V = 0, p-value < 2.2e-16
## alternative hypothesis: true location shift is not equal to 0
##
##
## Wilcoxon signed-rank test results for microbusiness_density and pct_college :
##
## Wilcoxon signed rank test with continuity correction
##
## data: merged_df_new[[pair[1]]] and merged_df_new[[pair[2]]]
## V = 6780, p-value < 2.2e-16
## alternative hypothesis: true location shift is not equal to 0
##
##
## Wilcoxon signed-rank test results for microbusiness_density and pct_foreign_born :
##
## Wilcoxon signed rank test with continuity correction
##
## data: merged_df_new[[pair[1]]] and merged_df_new[[pair[2]]]
## V = 2843324130, p-value < 2.2e-16
## alternative hypothesis: true location shift is not equal to 0
##
##
## Wilcoxon signed-rank test results for microbusiness_density and pct_it_workers :
##
## Wilcoxon signed rank test with continuity correction
##
## data: merged_df_new[[pair[1]]] and merged_df_new[[pair[2]]]
## V = 5996103713, p-value < 2.2e-16
## alternative hypothesis: true location shift is not equal to 0
##
##
## Wilcoxon signed-rank test results for microbusiness_density and median_hh_inc :
##
## Wilcoxon signed rank test with continuity correction
##
## data: merged_df_new[[pair[1]]] and merged_df_new[[pair[2]]]
## V = 0, p-value < 2.2e-16
## alternative hypothesis: true location shift is not equal to 0# Specify a list of column pairs to compare
col_pairs <- list(c("microbusiness_density", "pct_bb"), c("microbusiness_density", "pct_college"), c("microbusiness_density", "pct_foreign_born"), c("microbusiness_density", "pct_it_workers"), c("microbusiness_density", "median_hh_inc"))
# Loop through each column pair and perform the Wilcoxon rank sum test
for (pair in col_pairs) {
test_result <- wilcox.test(merged_df_new[[pair[1]]], merged_df_new[[pair[2]]], paired = FALSE)
cat(paste("Wilcoxon rank-sum test results for", pair[1], "and", pair[2], ":\n"))
print(test_result)
cat("\n")
}## Wilcoxon rank-sum test results for microbusiness_density and pct_bb :
##
## Wilcoxon rank sum test with continuity correction
##
## data: merged_df_new[[pair[1]]] and merged_df_new[[pair[2]]]
## W = 0, p-value < 2.2e-16
## alternative hypothesis: true location shift is not equal to 0
##
##
## Wilcoxon rank-sum test results for microbusiness_density and pct_college :
##
## Wilcoxon rank sum test with continuity correction
##
## data: merged_df_new[[pair[1]]] and merged_df_new[[pair[2]]]
## W = 112644499, p-value < 2.2e-16
## alternative hypothesis: true location shift is not equal to 0
##
##
## Wilcoxon rank-sum test results for microbusiness_density and pct_foreign_born :
##
## Wilcoxon rank sum test with continuity correction
##
## data: merged_df_new[[pair[1]]] and merged_df_new[[pair[2]]]
## W = 6244818672, p-value < 2.2e-16
## alternative hypothesis: true location shift is not equal to 0
##
##
## Wilcoxon rank-sum test results for microbusiness_density and pct_it_workers :
##
## Wilcoxon rank sum test with continuity correction
##
## data: merged_df_new[[pair[1]]] and merged_df_new[[pair[2]]]
## W = 1.0468e+10, p-value < 2.2e-16
## alternative hypothesis: true location shift is not equal to 0
##
##
## Wilcoxon rank-sum test results for microbusiness_density and median_hh_inc :
##
## Wilcoxon rank sum test with continuity correction
##
## data: merged_df_new[[pair[1]]] and merged_df_new[[pair[2]]]
## W = 0, p-value < 2.2e-16
## alternative hypothesis: true location shift is not equal to 0The results show that for each pair of columns, the p-value is less than the significance level of 0.05, which means that we reject the null hypothesis that the median difference between the two columns is zero. Instead, we conclude that there is a statistically significant difference between the two columns.
The results suggest that there is evidence to support the hypothesis that the population median of each column is different from the population median of microbusiness_density.
kernel regression
# create a vector of region names and their corresponding codes
region_codes <- c("new england" = 1,
"mideast" = 2,
"great lakes" = 3,
"plains" = 4,
"southeast" = 5,
"southwest" = 6,
"rocky mountain" = 7,
"far west" = 8)
# use the `match()` function to find the region code for each row in `merged_df_new$region`
merged_df_new$region_code <- match(merged_df_new$region, names(region_codes))
merged_df_clean$region_code <- match(merged_df_clean$region, names(region_codes))
# create a vector of state names and their corresponding codes
state_codes <- sort(unique(merged_df_new$state))
state_codes <- setNames(1:length(state_codes), state_codes)
# use the `match()` function to find the state code for each row in `merged_df_new$state`
merged_df_new$state_code <- match(merged_df_new$state, names(state_codes))
state_codes <- sort(unique(merged_df_clean$state))
state_codes <- setNames(1:length(state_codes), state_codes)
merged_df_clean$state_code <- match(merged_df_clean$state, names(state_codes))
# print head of the updated dataframe
head(merged_df_new)## row_id cfips county state first_day_of_month
## 1 1001_2019-08-01 1001 autauga county alabama 2019-08-01
## 2 1001_2019-09-01 1001 autauga county alabama 2019-09-01
## 3 1001_2019-10-01 1001 autauga county alabama 2019-10-01
## 4 1001_2019-11-01 1001 autauga county alabama 2019-11-01
## 5 1001_2019-12-01 1001 autauga county alabama 2019-12-01
## 6 1001_2020-01-01 1001 autauga county alabama 2020-01-01
## microbusiness_density active year_month year month pct_bb pct_college
## 1 3.007682 1249 2019-08 2019 8 76.6 14.5
## 2 2.884870 1198 2019-09 2019 9 76.6 14.5
## 3 3.055843 1269 2019-10 2019 10 76.6 14.5
## 4 2.993233 1243 2019-11 2019 11 76.6 14.5
## 5 2.993233 1243 2019-12 2019 12 76.6 14.5
## 6 2.969090 1242 2020-01 2020 1 78.9 15.9
## pct_foreign_born pct_it_workers median_hh_inc region region_code
## 1 2.1 1.3 55317 southeast 5
## 2 2.1 1.3 55317 southeast 5
## 3 2.1 1.3 55317 southeast 5
## 4 2.1 1.3 55317 southeast 5
## 5 2.1 1.3 55317 southeast 5
## 6 2.0 1.1 58786 southeast 5
## state_code
## 1 1
## 2 1
## 3 1
## 4 1
## 5 1
## 6 1merged_df_new |>
GGally::ggpairs(columns = c(17,18,2))## Registered S3 method overwritten by 'GGally':
## method from
## +.gg ggplot2
# Select the columns with numeric data
numeric_cols <- c("cfips", "state_code", "region_code", "microbusiness_density", "active", "year", "month", "pct_bb", "pct_college", "pct_foreign_born", "pct_it_workers", "median_hh_inc")
# Subset the dataframe with the selected columns
merged_df_numeric <- merged_df_new[, numeric_cols]
# Calculate the correlation matrix
cor_matrix <- cor(merged_df_numeric, use="pairwise.complete.obs")
# Plot the correlation matrix using ggcorrplot
ggcorrplot(cor_matrix,
hc.order = TRUE,
type = "lower",
method = "square",
lab = TRUE,
lab_size = 3,
title = "Correlation Plot of merged_df_new",
colors = c("#6D9EC1", "#FAC200", "#FA5252"),
ggtheme = ggplot2::theme_gray,
show.legend = TRUE)
# Select the columns with numeric data
numeric_cols <- c("cfips", "state_code", "region_code", "microbusiness_density", "active", "year", "month", "pct_bb", "pct_college", "pct_foreign_born", "pct_it_workers", "median_hh_inc")
# Subset the dataframe with the selected columns
merged_df_numeric <- merged_df_clean[, numeric_cols]
# Calculate the correlation matrix
cor_matrix <- cor(merged_df_numeric, use="pairwise.complete.obs")
# Plot the correlation matrix using ggcorrplot
ggcorrplot(cor_matrix,
hc.order = TRUE,
type = "lower",
method = "square",
lab = TRUE,
lab_size = 3,
title = "Correlation Plot of merged_df_clean",
colors = c("#6D9EC1", "#FAC200", "#FA5252"),
ggtheme = ggplot2::theme_gray,
show.legend = TRUE)
The cfips column and state_code have a
completely positive correlation. So, we will remove the redundant
feature state_code. Also, pct_bb strongly
correlates with median_hh_inc and pct_college.
Also, pct_college strongly correlates with
microbusiness_density, median_hh_inc and
pct_bb. As features with moderate strong and strong
correlation are redundant, we will remove these features
(pct_bb and pct_college) before further
analysis. Now, we draw the new correlation plot.
# Select the columns with numeric data (not including "state_code", "pct_bb", "pct_college")
numeric_cols <- c("cfips", "region_code", "microbusiness_density", "active", "year", "month", "pct_foreign_born", "pct_it_workers", "median_hh_inc")
# Subset the dataframe with the selected columns
merged_df_numeric <- merged_df_new[, numeric_cols]
# Calculate the correlation matrix
cor_matrix <- cor(merged_df_numeric, use="pairwise.complete.obs")
# Plot the correlation matrix using ggcorrplot
ggcorrplot(cor_matrix,
hc.order = TRUE,
type = "lower",
method = "square",
lab = TRUE,
lab_size = 3,
title = "Correlation Plot of merged_df_new",
colors = c("#6D9EC1", "#FAC200", "#FA5252"),
ggtheme = ggplot2::theme_gray,
show.legend = TRUE)
3.10. Feature Importance Using Random Forest
# Split the dataset into training and testing sets
set.seed(92) # for reproducibility
train_index <- sample(nrow(merged_df_new), 0.7 * nrow(merged_df_new))
train_data <- merged_df_new[train_index, ]
test_data <- merged_df_new[-train_index, ]
# Build the random forest model
model <- randomForest(microbusiness_density ~ cfips + region_code + active + year + month + pct_foreign_born + pct_it_workers + median_hh_inc,
data = train_data)
# Make predictions on the test set
predictions <- predict(model, test_data)
# Check the accuracy of the model
# accuracy <- sum(predictions == test_data$microbusiness_density) / nrow(test_data)
# cat("Accuracy:", accuracy, "\n")
# Plot the variable importance
varImpPlot(model, main = "Variable Importance Plot")
# Load revealed_test.csv into a dataframe
revealed_test_df <- read.csv("./datasets/revealed_test.csv")
# Change first_day_of_month format in "revealed_test_df" to Date
revealed_test_df$first_day_of_month <- as.Date(revealed_test_df$first_day_of_month)4. Time Series Forecasting
4.1 Exponential Forecasting
Forecasts produced using exponential smoothing methods are weighted averages of past observations, with the weights decaying exponentially as the observations get older. In other words, the more recent the observation the higher the associated weight. This framework generates reliable forecasts quickly and for a wide range of time series, which is a great advantage and of major importance to applications in industry. ### 4.1.1. Simple Exponential Smoothing Forecast Exponential smoothing is a general technique for smoothing time series data by giving more weight to recent observations. The simplest of the exponentially smoothing methods is naturally called simple exponential smoothing (SES). This method is suitable for forecasting data with no clear trend or seasonal pattern. (There is a grow in the last few years, which might suggest a trend. We will consider whether a trended method would be better for this series later.)
# Select relevant predictor columns
# predictors <- merged_df_new[, c("microbusiness_density", "cfips")]
merged_df_ts <- merged_df_clean %>%
group_by(first_day_of_month) %>%
summarise(microbusiness_density = mean(microbusiness_density))
# Convert data to time series format
ts_data <- ts(merged_df_ts$microbusiness_density, start = c(2019, 8), frequency = 12)# fit a simple exponential smoothing model to the time series data
fit <- ets(ts_data, model = "ANN")
# generate forecasts for the time series data using the fitted model
forecast_values <- forecast::forecast(fit, h = 8)plot(forecast_values, main = "Simple Exponential Smoothing Forecast", xlab = "Year", ylab = "Microbusiness Density")
lines(forecast_values$fitted, col = "red")
lines(ts_data, col = "blue")
legend("bottomleft", legend = c("Forecast", "Actual"), col = c("red", "blue"), lty = 1)
The forecasts for the period 11/2022 to 06/2023 are plotted in above.
Also, plotted are one-step-ahead fitted values alongside the data over
the period 08/2019 to 10/2022.
# Split data into training and testing sets
train_data <- window(ts_data, end = c(2022, 2))
test_data <- window(ts_data, start = c(2022, 3))
# Train neural network autoregression model
nnetar_model <- nnetar(ts_data)
# Make forecasts using the trained model
forecast_data <- forecast::forecast(nnetar_model, h = length(test_data))# Convert data to time series format
ts_data <- ts(merged_df_ts$microbusiness_density, start = c(2019, 8), frequency = 12)
# Split data into training and testing sets
train_data <- window(ts_data, end = c(2022, 2))
test_data <- window(ts_data, start = c(2022, 3))
# Fit a neural network autoregression model with error("A"), trend("N"), season("N") preferences
nnetar_model <- nnetar(train_data, lambda = 0, P = 12, size = 10, repeats = 10,
decay = 0.5, maxit = 1000, trace = TRUE,
entropy = FALSE, parallel = FALSE, xreg = NULL)## # weights: 41
## initial value 21.283645
## iter 10 value 11.004232
## iter 20 value 10.950528
## iter 30 value 10.940432
## iter 40 value 10.939499
## final value 10.939493
## converged
## # weights: 41
## initial value 59.692453
## iter 10 value 11.964849
## iter 20 value 10.974613
## iter 30 value 10.949670
## iter 40 value 10.945596
## iter 50 value 10.941198
## iter 60 value 10.939534
## final value 10.939493
## converged
## # weights: 41
## initial value 70.392818
## iter 10 value 11.771520
## iter 20 value 10.980551
## iter 30 value 10.943868
## iter 40 value 10.939699
## iter 50 value 10.939518
## final value 10.939493
## converged
## # weights: 41
## initial value 26.849765
## iter 10 value 10.989322
## iter 20 value 10.955714
## iter 30 value 10.951777
## iter 40 value 10.951562
## final value 10.951541
## converged
## # weights: 41
## initial value 32.025911
## iter 10 value 11.050677
## iter 20 value 10.979900
## iter 30 value 10.942657
## iter 40 value 10.939626
## iter 50 value 10.939493
## final value 10.939493
## converged
## # weights: 41
## initial value 42.111868
## iter 10 value 11.083042
## iter 20 value 10.953153
## iter 30 value 10.951628
## iter 40 value 10.951561
## iter 50 value 10.951540
## iter 50 value 10.951540
## iter 50 value 10.951540
## final value 10.951540
## converged
## # weights: 41
## initial value 51.452718
## iter 10 value 13.681090
## iter 20 value 10.979947
## iter 30 value 10.958008
## iter 40 value 10.954194
## iter 50 value 10.952654
## iter 60 value 10.951666
## iter 70 value 10.951540
## iter 70 value 10.951540
## iter 70 value 10.951540
## final value 10.951540
## converged
## # weights: 41
## initial value 38.123377
## iter 10 value 11.066611
## iter 20 value 10.957299
## iter 30 value 10.951926
## iter 40 value 10.951545
## final value 10.951540
## converged
## # weights: 41
## initial value 33.945638
## iter 10 value 11.005029
## iter 20 value 10.957049
## iter 30 value 10.951637
## iter 40 value 10.951559
## iter 50 value 10.951540
## final value 10.951540
## converged
## # weights: 41
## initial value 53.766483
## iter 10 value 12.197989
## iter 20 value 10.958533
## iter 30 value 10.943320
## iter 40 value 10.941039
## iter 50 value 10.939557
## iter 60 value 10.939496
## final value 10.939493
## converged# Make predictions using the fitted model
nnetar_fc <- forecast::forecast(nnetar_model, h = length(test_data))
# Print the forecasted values
print(nnetar_fc$mean)## Mar Apr May Jun Jul Aug Sep Oct
## 2022 2.804899 2.811903 2.816620 2.819850 2.822088 2.823652 2.824751 2.825525# Plot actual and predicted values for comparison
plot(ts_data, type = "l", main = "Neural Network Autoregression")
#lines(nnetar_fc$mean, col = "blue")
legend("topleft", legend = c("Actual", "Predicted"), col = c("black", "blue"), lty = 1)
# Calculate accuracy measures
forecast::accuracy(nnetar_fc$mean, test_data)## ME RMSE MAE MPE MAPE ACF1
## Test set 0.01666848 0.02306722 0.0186722 0.5839484 0.6552904 0.3798398
## Theil's U
## Test set 1.367118# Calculate forecast errors
nnetar_errors <- test_data - nnetar_fc$mean
mean(nnetar_errors)## [1] 0.01666848sd(nnetar_errors)## [1] 0.01704644plot(nnetar_fc, main = "Neural network autoregression Forecast", xlab = "Year", ylab = "Microbusiness Density")
lines(nnetar_fc$mean, col = "red")
#lines(ts_data, col = "blue")
legend("bottomleft", legend = c("Forecast", "Actual"), col = c("red", "blue"), lty = 1)
# Plot forecasts and actual values
plot(forecast_data, main = "Neural Network Autoregression Forecasts")
lines(test_data, col = "blue")